Student thinking path dynamic aggregation method based on polymorphic Bayesian cluster

Abstract

The invention discloses a student thinking path dynamic aggregation method based on a polymorphic Bayesian cluster. The method comprises the following steps: S1, acquiring behavior data and cognitive data of students in a learning process; s2, preprocessing the collected learning behavior data and cognitive data; s3, constructing a knowledge point graph; s4, initializing parameters of the student thinking path dynamic aggregation model; s5, generating thinking path marks associated with the knowledge points; s6, identifying weak links and non-linear jump logic of the students in the knowledge point association chain; s7, forming a new thinking path aggregation result; and S8, according to the dynamically optimized thinking path aggregation result of the students, generating teaching feedback for learning weak links of the students, including suggested reinforcing knowledge points, optimized learning sequences and customized learning tasks. According to the method, the learning sequence and the jumping logic scheme can be adjusted according to the thinking path change of the current learning stage of the student, and more accurate personalized learning suggestions and real-time teaching intervention support are provided for the student.

Description

Technical Field

[0001] The present invention relates to the field of auxiliary learning technology, and in particular to a method for dynamically aggregating student thinking paths based on polymorphic Bayesian clustering. Background Art

[0002] In the existing field of educational technology, the analysis of students' thinking paths usually relies on static data analysis methods. Static data analysis methods infer students' learning patterns or thinking paths by performing global statistics and induction on students' historical learning behavior data. However, static analysis methods have significant limitations and it is difficult to capture the changes in students' thinking paths in the dynamic learning process in real time. Students may show jumping thinking and logical transfer of error correction in the process of solving problems, or their logical deduction paths may change significantly as the learning tasks progress. Dynamic changes are often ignored or weakened in traditional static methods.

[0003] In order to address the shortcomings of static analysis, some dynamic clustering methods and student behavior modeling technologies based on machine learning have begun to be introduced into the field of education. Machine learning can, to a certain extent, track behavioral changes in the learning process in real time. Existing dynamic clustering methods are mostly limited to a single data source and are difficult to integrate students' multimodal learning data. In addition, existing technologies usually lack in-depth analysis of the structure of learning content and cannot effectively model the relationship between students' thinking paths and knowledge points.

[0004] Another significant flaw of existing technologies is the limitation of personalized teaching feedback. Many educational technology systems only record and simply evaluate students' learning behaviors, but it is difficult to deeply explore the logical chains and potential thinking patterns in students' problem-solving process. This makes it difficult for teachers to adjust teaching strategies based on the analysis results generated by existing systems, and it is impossible to provide students with accurate personalized learning suggestions, which affects teaching effectiveness and learning efficiency. Summary of the invention

[0005] One purpose of the present invention is to propose a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering. The present invention can adjust the learning sequence and jumping logic scheme according to the changes in the thinking paths of students in the current learning stage, and provide students with more accurate personalized learning suggestions and real-time teaching intervention support.

[0006] A method for dynamically aggregating student thinking paths based on polymorphic Bayesian clustering according to an embodiment of the present invention includes the following steps:

[0007] S1. Obtain students’ behavioral and cognitive data during the learning process;

[0008] S2. Preprocess the collected learning behavior data and cognitive data;

[0009] S3. Construct a knowledge point map based on the predefined subject knowledge point structure, learning behavior data and cognitive data;

[0010] S4. Use the polymorphic Bayesian clustering algorithm to construct a dynamic aggregation model of students' thinking paths and initialize the parameters of the dynamic aggregation model of students' thinking paths;

[0011] S5. Input the preprocessed learning behavior data and cognitive data into the student thinking path dynamic aggregation model, and cluster the student's learning behavior data and cognitive data in real time in combination with the node relationship in the knowledge point map, dynamically capture the changes in the student's thinking path, and generate thinking path tags associated with the knowledge points;

[0012] S6. Based on the results of dynamic clustering analysis, combined with the learning behavior data and cognitive data of each node in the knowledge point map, calculate the learning mastery of each knowledge point and its thinking jump pattern across knowledge points, and identify the weak links and nonlinear jump logic in the knowledge point association chain of students;

[0013] S7. Analyze the identified weak links and jumpy thinking paths, optimize students’ learning paths by adjusting the node weights in the knowledge point map and the parameters of dynamic clustering, and form new thinking path aggregation results;

[0014] S8. Based on the aggregation results of students’ thinking paths after dynamic optimization, generate teaching feedback targeting students’ weak learning links, including recommended supplementary knowledge points, optimized learning sequence and customized learning tasks.

[0015] Optionally, the S1 specifically includes the following sub-steps:

[0016] S11. Collect students' behavior data during the learning process, including problem-solving steps and problem-solving time information. step represents the sequence of steps that students go through when solving each question, and the problem-solving time information T step It indicates the time students spend solving each operation;

[0017] S12. Collect students' cognitive data during the learning process, including students' answer accuracy, problem-solving logic structure and knowledge point relevance information, answer accuracy R c It is defined as the ratio of the number of correct answers given by students to the total number of answers given to a specific question or knowledge point. logic Indicates the reasoning path used by students in answering questions, and the knowledge point relevance information A k It indicates the students’ mastery of knowledge point k, which is defined as the proportion of the knowledge point correctly applied in the problem-solving process;

[0018] S13. Integrate the data obtained from the behavior data collection module and the cognitive data collection module to obtain the behavior data set D1 and the cognitive data set D2:

[0019] D1={S step ,T step};

[0020] D2={R c ,G logic ,A k}.

[0021] Optionally, S3 specifically includes the following sub-steps:

[0022] S31. Define the knowledge point set K = {k1, k2, ..., k m}, where k i represents the i-th knowledge point, based on the learning behavior dataset D1 and the cognitive dataset D2 for each knowledge point k i Constructing feature vectors Eigenvector Including the frequency of students involving knowledge points in the sequence of problem-solving steps Average time students spend solving problems in the problem-solving steps involving knowledge points and students’ mastery of knowledge points

[0023] S32. Based on students' logical structure of problem solving G logic and knowledge mastery level A k , calculate the knowledge point k i With knowledge point k j The association weight w ij :

[0024]

[0025] in, Indicates that students are solving the problem in the logical structure G logic From knowledge point k i To knowledge point k j The number of path occurrences, is the maximum number of path occurrences among all knowledge point pairs, and For students to understand the knowledge point k i and k j The degree of mastery, Represents knowledge point k i and k j The semantic similarity between:

[0026]

[0027] in, and are knowledge points k respectively i and k j The characteristic vector of represents the modulus of the feature vector, θ, φ, ψ are the weight coefficients of the association weight, which are used to balance the influence of path frequency, mastery degree and semantic similarity in the calculation of association weight;

[0028] S33. Constructing knowledge point graph:

[0029] G knowledge =(K,E,W);

[0030] Where K is the knowledge point node set, E = {(k i ,k j )|w ij >0,k i ,k j ∈K} is the set of associated edges between knowledge points, indicating that there is an associated relationship between knowledge points. ij ∣(k i ,k j )∈E} is the set of association weights;

[0031] S34. Calculate each knowledge point k i Importance index The importance index represents the centrality of the knowledge point in the graph:

[0032]

[0033] Among them, deg(k i ) is the knowledge point k i The degree of i The number of connected edges, w ij is knowledge point k i With knowledge point k j The weight of the association between .

[0034] Optionally, the S4 specifically includes the following sub-steps:

[0035] S41. Constructing a dynamic aggregation model of students' thinking paths based on polymorphic Bayesian clustering algorithm M SP The dynamic aggregation model of students' thinking paths consists of latent variables Z, observed variables X, prior distribution P(Z) and conditional probability distribution P(X|Z), where latent variables represent students' potential thinking path categories, observed variables represent students' behavioral data and cognitive data in the learning process, prior distribution represents the prior probability of the latent category, which is used to initialize the distribution hypothesis of students' thinking path categories, and conditional probability distribution represents the distribution of observed data X under the condition of given latent category Z, which is used to describe the characteristics of data in different categories;

[0036] S42. Initialize the prior distribution P(Z) and conditional probability distribution P(X|Z) of the dynamic aggregation model of students' thinking paths based on their learning behavior data and cognitive data;

[0037] S43. Combined with knowledge point graph G knowledge , take the weight W in the knowledge point map as the constraint condition of the dynamic aggregation model of the student's thinking path, and modify the parameters in the conditional probability distribution P(X|Z):

[0038]

[0039] Among them, w ij Represents knowledge point k i With k j The association weight, x j is knowledge point k j Observed value of

[0040] S44. Combine the prior distribution P(Z) and the conditional probability distribution P(X|Z) to calculate the joint probability distribution P(Z,X) of the dynamic aggregation model of student thinking paths:

[0041] P(Z,X)=P(Z)·P(X|Z).

[0042] Optionally, S5 specifically includes the following sub-steps:

[0043] S51. Input the preprocessed learning behavior dataset D1 and cognitive dataset D2 into the student thinking path dynamic aggregation model M SP , the input data X is expressed as:

[0044] X={x1,x2,…,x n},x i ∈D1∪D22;

[0045] Among them, x i Represents specific observations related to student behavior or cognition;

[0046] S52. Using the dynamic aggregation model of students' thinking paths M SP Perform real-time clustering on the input data X to generate a latent class label z for each observation i :

[0047]

[0048] Where P(Z=z|X=x i ) is calculated by Bayesian inference, combining the prior distribution P(Z) and the conditional probability distribution P(X|Z):

[0049]

[0050] Among them, z i Indicates the potential thinking path category of students under the current observation value;

[0051] S53. Using the knowledge point graph G knowledge The node relationships and weight constraints in ij Correct the clustering result Z and calculate the corrected category distribution P ′ (Z=z|X):

[0052]

[0053] Among them, λ is a tuning parameter used to balance the relationship between clustering results and knowledge point graph constraints, neighbor(i) represents the set of nodes adjacent to node i, and δ(z i ,z j ) is the consistency discriminant function, when z i =z j The value is 1 when it is, otherwise it is 0;

[0054] S54. Generate a student thinking path tag set P associated with the knowledge point based on the modified clustering result Z path , each marker p i Indicates the main thinking path of students in the current time period, according to the knowledge point map G knowledge The path association calculates the path with the largest weight:

[0055]

[0056] in, For students in the knowledge point map G knowledge The set of thinking paths in the ij Represents the knowledge point k in the path i and k j The associated weight of .

[0057] Optionally, the S6 specifically includes the following sub-steps:

[0058] S61. Combined with knowledge point graph G knowledge The node attributes and dynamic clustering results Z of the students are calculated for each knowledge point k i Learning mastery

[0059]

[0060] in, Representation and knowledge point k i The relevant set of observation data, δ(z j ,zcorrect ) is the correctness discriminant function, when the clustering result z j It takes the value of 1 when the student has mastered it correctly, otherwise it takes the value of 0. is the same as knowledge point k i The total number of relevant observations, P ′ (Z=z j |X=x j ) represents the modified latent class probability distribution;

[0061] S62. Using the knowledge point graph G knowledge The edge weight w ij and dynamic clustering result Z to calculate the student's knowledge point k i and k j The thinking jump mode between ij :

[0062]

[0063] Among them, H ij Indicates that students learn from knowledge point k i Jump to k j The strength of association, x p and x q are respectively related to knowledge point k i and k j The relevant observation value, E is the set of associated edges in the knowledge point graph;

[0064] S63. Based on learning mastery and thinking jump mode H ij Identify the weak links in the knowledge point association chain of students and calculate the weak link score S weak :

[0065]

[0066] Among them, S weak (k i ,k j ) represents knowledge point k i to k j The weak link score is weak (k i ,k j ) exceeds a preset threshold, marking the chain as a weak link;

[0067] S64. Students in the knowledge point map G knowledge The path transfer mode in the nonlinear jump logic probability P is calculated nonlinear :

[0068]

[0069] in, Represents a set of expected paths that conform to normal logic. Represents the student's nonlinear jump path.

[0070] Optionally, the S7 specifically includes the following sub-steps:

[0071] S71. Locate the weak parts of the associated chains in the knowledge point map based on the identified weak links and the corresponding learning behavior data and cognitive data, including nodes with low mastery of key knowledge points and chains with weaker association weights between nodes;

[0072] S72. Optimize the association weights of weak links in the knowledge point map based on the weak link analysis results, and increase the connection weights between highly correlated nodes;

[0073] S73. Update the key parameters of the student thinking path dynamic aggregation model based on the adjusted knowledge point map, and recalculate the observed data distribution and potential category distribution in the student thinking path dynamic aggregation model;

[0074] S74. Generate an optimized learning path based on the adjusted knowledge point map and the results of the student thinking path dynamic aggregation model, determine the knowledge points that students should focus on in the new learning stage, and mark the learning sequence and jump logic adjustment plan;

[0075] S75. Store the optimized knowledge point map, student thinking path dynamic aggregation model parameters and learning path aggregation results in the student file management system, and generate a learning path report.

[0076] The beneficial effects of the present invention are:

[0077] (1) The present invention combines the polymorphic Bayesian clustering algorithm with the dynamic aggregation model of students' thinking paths, which can effectively integrate students' behavioral data and cognitive data, and combine with the knowledge point map for dynamic constraints, breaking through the limitations of traditional single-modal data analysis and realizing the deep fusion and real-time dynamic modeling of multimodal data. Compared with traditional static analysis, it can capture the real-time changing thinking paths of students during the learning process, significantly improve the accuracy and timeliness of data analysis, and has significant advantages in dealing with leap learning behaviors across knowledge points.

[0078] (2) The present invention optimizes the conditional probability distribution and clustering results of the polymorphic Bayesian clustering model by using the node relationships and association weights between knowledge points through the knowledge point graph. It can dynamically adjust the parameters of the clustering model according to the students' interaction frequency and mastery of different knowledge points during the learning process, effectively reducing the errors and noise in the clustering process. In the scenario of processing complex knowledge point networks, the dynamic constraints of the knowledge point graph are combined to make the students' thinking path analysis results more in line with the actual learning logic.

[0079] (3) The present invention uses a path analysis and optimization algorithm to generate personalized learning paths and teaching feedback in real time based on dynamic clustering results and the positioning of weak links in the knowledge point map. Compared with the existing technology that relies on static data to generate unified feedback, the present invention can adjust the learning sequence and jumping logic plan according to the changes in the thinking path of students in the current learning stage, thereby providing students with more accurate personalized learning suggestions and real-time teaching intervention support. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0081] Figure 1 This is a flow chart of a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering proposed by the present invention. DETAILED DESCRIPTION

[0082] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0083] refer to Figure 1 , a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering, comprising the following steps:

[0084] S1. Obtain students’ behavioral and cognitive data during the learning process;

[0085] S2. Preprocess the collected learning behavior data and cognitive data;

[0086] S3. Construct a knowledge point map based on the predefined subject knowledge point structure, learning behavior data and cognitive data;

[0087] S4. Use the polymorphic Bayesian clustering algorithm to construct a dynamic aggregation model of students' thinking paths and initialize the parameters of the dynamic aggregation model of students' thinking paths;

[0088] S5. Input the preprocessed learning behavior data and cognitive data into the student thinking path dynamic aggregation model, and cluster the student's learning behavior data and cognitive data in real time in combination with the node relationship in the knowledge point map, dynamically capture the changes in the student's thinking path, and generate thinking path tags associated with the knowledge points;

[0089] S6. Based on the results of dynamic clustering analysis, combined with the learning behavior data and cognitive data of each node in the knowledge point map, calculate the learning mastery of each knowledge point and its thinking jump pattern across knowledge points, and identify the weak links and nonlinear jump logic in the knowledge point association chain of students;

[0090] S7. Analyze the identified weak links and jumpy thinking paths, optimize students’ learning paths by adjusting the node weights in the knowledge point map and the parameters of dynamic clustering, and form new thinking path aggregation results;

[0091] S8. Based on the aggregation results of students’ thinking paths after dynamic optimization, generate teaching feedback targeting students’ weak learning links, including recommended supplementary knowledge points, optimized learning sequence and customized learning tasks.

[0092] In this implementation, S1 specifically includes the following sub-steps:

[0093] S11. Collect students' behavior data during the learning process, including problem-solving steps and problem-solving time information. step represents the sequence of steps that students go through when solving each question, and the problem-solving time information T step It indicates the time students spend solving each operation;

[0094] S12. Collect students’ cognitive data during the learning process. Cognitive data includes students’ correct answer rate, problem-solving logic structure and knowledge point relevance information. Correct answer rate R c It is defined as the ratio of the number of correct answers given by students to the total number of answers given to a specific question or knowledge point. logic Indicates the reasoning path used by students in answering questions, and the knowledge point relevance information A k It indicates the students’ mastery of knowledge point k, which is defined as the proportion of the knowledge point correctly applied in the problem-solving process;

[0095] S13. Integrate the data obtained from the behavior data collection module and the cognitive data collection module to obtain the behavior data set D1 and the cognitive data set D2:

[0096] D1={S step ,T step};

[0097] D2={R c ,G logic ,A k}.

[0098] In this implementation, S3 specifically includes the following sub-steps:

[0099] S31. Define the knowledge point set K = {k1, k2, ..., k m}, where k i represents the i-th knowledge point, based on the learning behavior dataset D1 and the cognitive dataset D2 for each knowledge point k i Constructing feature vectors Eigenvector Including the frequency of students involving knowledge points in the sequence of problem-solving steps Average time students spend solving problems in the problem-solving steps involving knowledge points and students’ mastery of knowledge points

[0100] S32. Based on students' logical structure of problem solving G logic and knowledge mastery level A k , calculate the knowledge point k i With knowledge point k j The association weight w ij :

[0101]

[0102] in, Indicates that students are solving the problem in the logical structure G logic From knowledge point k i To knowledge point k j The number of path occurrences, is the maximum number of path occurrences among all knowledge point pairs, and For students to understand the knowledge point k i and k j The degree of mastery, Represents knowledge point k i and k j The semantic similarity between:

[0103]

[0104] in, and are knowledge points k respectively i and k j The characteristic vector of represents the modulus of the feature vector, θ, φ, ψ are the weight coefficients of the association weight, which are used to balance the influence of path frequency, mastery degree and semantic similarity in the calculation of association weight;

[0105] S33. Constructing knowledge point graph:

[0106] G knowledge =(K,E,W);

[0107] Where K is the knowledge point node set, E = {(k i ,k j )|w ij >0,k i ,k j ∈K} is the set of associated edges between knowledge points, indicating that there is an associated relationship between knowledge points. ij ∣(k i ,k j )∈E} is the set of association weights;

[0108] S34. Calculate each knowledge point k i Importance index The importance index represents the centrality of the knowledge point in the graph:

[0109]

[0110] Among them, deg(k i ) is the knowledge point k i The degree of i The number of connected edges, w ij is knowledge point k i With knowledge point k j The weight of the association between .

[0111] In this implementation, S4 specifically includes the following sub-steps:

[0112] S41. Constructing a dynamic aggregation model of students' thinking paths based on polymorphic Bayesian clustering algorithm M SP The dynamic aggregation model of students' thinking paths consists of latent variables Z, observed variables X, prior distribution P(Z) and conditional probability distribution P(X|Z), where latent variables represent students' potential thinking path categories, observed variables represent students' behavioral data and cognitive data in the learning process, prior distribution represents the prior probability of the latent category, which is used to initialize the distribution hypothesis of students' thinking path categories, and conditional probability distribution represents the distribution of observed data X under the condition of given latent category Z, which is used to describe the characteristics of data in different categories;

[0113] S42. Initialize the prior distribution P(Z) and conditional probability distribution P(X|Z) of the dynamic aggregation model of students' thinking paths based on their learning behavior data and cognitive data;

[0114] S43. Combined with knowledge point graph G knowledge , take the weight W in the knowledge point map as the constraint condition of the dynamic aggregation model of the student's thinking path, and modify the parameters in the conditional probability distribution P(X|Z):

[0115]

[0116] Among them, w ij Represents knowledge point k i With k j The association weight, x j is knowledge point k j Observed value of

[0117] S44. Combine the prior distribution P(Z) and the conditional probability distribution P(X|Z) to calculate the joint probability distribution P(Z,X) of the dynamic aggregation model of student thinking paths:

[0118] P(Z,X)=P(Z)·P(X|Z).

[0119] In this implementation, S5 specifically includes the following sub-steps:

[0120] S51. Input the preprocessed learning behavior dataset D1 and cognitive dataset D2 into the student thinking path dynamic aggregation model M SP , the input data X is expressed as:

[0121] X={x1,x2,…,x n},x i ∈D1∪D22;

[0122] Among them, x i Represents specific observations related to student behavior or cognition;

[0123] S52. Using the dynamic aggregation model of students' thinking paths M SP Perform real-time clustering on the input data X to generate a latent class label z for each observation i :

[0124]

[0125] Where P(Z=z|X=x i ) is calculated by Bayesian inference, combining the prior distribution P(Z) and the conditional probability distribution P(X|Z):

[0126]

[0127] Among them, z i Indicates the potential thinking path category of students under the current observation value;

[0128] S53. Using the knowledge point graph G knowledge The node relationships and weight constraints in ij Correct the clustering result Z and calculate the corrected category distribution P ′ (Z=z|X):

[0129]

[0130] Among them, λ is a tuning parameter used to balance the relationship between clustering results and knowledge point graph constraints, neighbor(i) represents the set of nodes adjacent to node i, and δ(z i ,z j ) is the consistency discriminant function, when z i =z j The value is 1 when it is, otherwise it is 0;

[0131] S54. Generate a student thinking path tag set P associated with the knowledge point based on the modified clustering result Z path , each marker p i Indicates the main thinking path of students in the current time period, according to the knowledge point map G knowledge The path association calculates the path with the largest weight:

[0132]

[0133] in, For students in the knowledge point map G knowledge The set of thinking paths in the ij Represents the knowledge point k in the path i and k j The associated weight of .

[0134] In this implementation, S6 specifically includes the following sub-steps:

[0135] S61. Combined with knowledge point graph G knowledge The node attributes and dynamic clustering results Z of the students are calculated for each knowledge point k i Learning mastery

[0136]

[0137] in, Representation and knowledge point k i The relevant set of observation data, δ(z j ,z correct ) is the correctness discriminant function, when the clustering result z j It takes the value of 1 when the student has mastered it correctly, otherwise it takes the value of 0. is the same as knowledge point k i The total number of relevant observations, P ′ (Z=z j |X=x j ) represents the modified latent class probability distribution;

[0138] S62. Using the knowledge point graph G knowledge The edge weight w ijand dynamic clustering result Z to calculate the student's knowledge point k i and k j The thinking jump mode between ij :

[0139]

[0140] Among them, H ij Indicates that students learn from knowledge point k i Jump to k j The strength of association, x p and x q are respectively related to knowledge point k i and k j The relevant observation value, E is the set of associated edges in the knowledge point graph;

[0141] S63. Based on learning mastery and thinking jump mode H ij Identify the weak links in the knowledge point association chain of students and calculate the weak link score S weak :

[0142]

[0143] Among them, S weak (k i ,k j ) represents knowledge point k i to k j The weak link score is weak (k i ,k j ) exceeds a preset threshold, marking the chain as a weak link;

[0144] S64. Students in the knowledge point map G knowledge The path transfer mode in the nonlinear jump logic probability P is calculated nonlinear :

[0145]

[0146] in, Represents a set of expected paths that conform to normal logic. Represents the student's nonlinear jump path.

[0147] In this implementation, S7 specifically includes the following sub-steps:

[0148] S71. Locate the weak parts of the associated chains in the knowledge point map based on the identified weak links and the corresponding learning behavior data and cognitive data, including nodes with low mastery of key knowledge points and chains with weaker association weights between nodes;

[0149] S72. Optimize the association weights of weak links in the knowledge point map based on the weak link analysis results, and increase the connection weights between highly correlated nodes;

[0150] S73. Update the key parameters of the student thinking path dynamic aggregation model based on the adjusted knowledge point map, and recalculate the observed data distribution and potential category distribution in the student thinking path dynamic aggregation model;

[0151] S74. Generate an optimized learning path based on the adjusted knowledge point map and the results of the student thinking path dynamic aggregation model, determine the knowledge points that students should focus on in the new learning stage, and mark the learning sequence and jump logic adjustment plan;

[0152] S75. Store the optimized knowledge point map, student thinking path dynamic aggregation model parameters and learning path aggregation results in the student file management system, and generate a learning path report.

[0153] Embodiment 1:

[0154] Embodiment On May 12, 2024, a key middle school conducted a two-week learning intervention experiment in the senior mathematics intensive class. The goal of the experiment was to improve students' mastery of key mathematical knowledge of functions, inequalities, and series through a dynamic aggregation method of students' thinking paths based on polymorphic Bayesian clustering, and to optimize their problem-solving logic and thinking paths.

[0155] On the morning of the first day of the experiment, student Li Ming completed a basic math test. The system collected and analyzed Li Ming's test data in real time. When Li Ming completed question 12 in the test, the system recorded the following key data:

[0156] Problem-solving step sequence S step ={s1,s2,s3,s4}, where s1 means trying to substitute, s2 means using formula to deduce, s3 means combining number line analysis, and s4 means getting a wrong answer;

[0157] The corresponding problem-solving time T step ={8s,15s,20s,5s};

[0158] Correct answer rate R c =0.33 (there are 6 similar questions in question 12, and Li Ming completed 2 of them correctly);

[0159] Knowledge point relevance A k =0.5 (accuracy rate of exercises related to the knowledge point “monotonicity of function”).

[0160] The system found through dynamic clustering analysis that Li Ming showed obvious logical jump patterns in the problem-solving process.knowledge The system locates that Li Ming has a low level of mastery of the two knowledge points of "function monotonicity" and "combination of function and inequality". At the same time, through the path association weight, it is found that Li Ming frequently makes mistakes when trying to derive the "range of inequality values" from "function monotonicity". The system automatically generates a learning report pointing out that Li Ming's problem lies in the confusion between monotonicity judgment and inequality boundary processing.

[0161] On the afternoon of May 13, the system generated a personalized learning path based on Li Ming's dynamic thinking path, including:

[0162] Strengthen training of 10 basic questions on "monotonicity of functions";

[0163] Focus on practicing 5 high-frequency test points of "Combining functions and inequalities", setting moderately challenging questions to test its logical chain;

[0164] Three real-time test questions were arranged, requiring Li Ming to record the monotonicity judgment process in detail, and the system automatically analyzed the rationality of its logical steps.

[0165] After Li Ming completed the personalized training, the system captured the following data changes in real time:

[0166] In the intensive training questions, the average length of the sequence of problem-solving steps was optimized from 4 steps to 3 steps, and redundant logic was reduced;

[0167] Knowledge point "Function monotonicity" mastery degree A k Improved to 0.8;

[0168] The logic jump frequency was reduced by 25%, and the error rate dropped from 33% to 12%.

[0169] In a classroom test on the morning of May 19, Li Ming completed a difficult function and inequality problem. The system recorded that he used the logical chain recommended by the dynamic learning path in the process of solving the problem, and obtained the correct answer in 63 seconds (35% less time than similar questions). The system further analyzed and found that Li Ming's path weight when deriving "inequality solving" from "monotonicity judgment" increased by 18%, proving that the dynamic learning path significantly optimized his thinking ability.

[0170] At the end of the experiment on May 26, the school conducted final tests on students in the experimental and control groups. The overall accuracy rate of Li Ming's experimental group increased from 63% in the previous test to 88%, while the control group increased by 17%. Li Ming's personal mastery of weak knowledge points improved by 25% and his accuracy rate in multiple logical deduction questions reached 95%, demonstrating the significant effectiveness of the system optimization path.

[0171] Through the examples, we can see how the method of the present invention dynamically captures students' learning problems in real educational scenarios, and optimizes the learning path through knowledge point maps and dynamic clustering analysis, thereby improving learning efficiency and effectiveness. The examples fully demonstrate the effectiveness and feasibility of the present invention in processing multimodal data and generating personalized teaching feedback.

[0172] The present invention combines the polymorphic Bayesian clustering algorithm with the dynamic aggregation model of students' thinking paths, can effectively integrate students' behavioral data and cognitive data, and combine with the knowledge point map for dynamic constraints, breaking through the limitations of traditional unimodal data analysis and realizing the deep fusion of multimodal data and real-time dynamic modeling. Compared with traditional static analysis, it can capture the real-time changing thinking paths of students during the learning process, significantly improve the accuracy and timeliness of data analysis, and has significant advantages in processing jumping learning behaviors across knowledge points. Experimental verification shows that the dynamic clustering accuracy is improved by more than 15% compared with traditional methods, and the delay in capturing dynamic changes is reduced to milliseconds.

[0173] The present invention optimizes the conditional probability distribution and clustering results of the polymorphic Bayesian clustering model by using the node relationship and association weights between knowledge points through the knowledge point graph, and can dynamically adjust the parameters of the clustering model according to the students' interaction frequency and mastery of different knowledge points during the learning process, effectively reducing errors and noise in the clustering process. In the scenario of processing complex knowledge point networks, combined with the dynamic constraints of the knowledge point graph, the students' thinking path analysis results are more in line with the actual learning logic. Experimental results show that after adopting the technology of the present invention, the prediction accuracy of the knowledge point mastery is improved by 20%, and a personalized path that is more in line with the students' learning status can be generated in a dynamic learning environment.

[0174] The present invention uses a path analysis and optimization algorithm, based on dynamic clustering results and the positioning of weak links in the knowledge point map, to generate personalized learning paths and teaching feedback in real time. Compared with the prior art that relies on static data to generate unified feedback, the present invention can adjust the learning sequence and jumping logic scheme according to the changes in the thinking path of students in the current learning stage, and provide students with more accurate personalized learning suggestions and real-time teaching intervention support. Experimental results show that after adopting the technology of the present invention, the students' knowledge point mastery rate is improved by an average of 18%, and the improvement speed of weak knowledge points is increased by 25%, which significantly improves the students' learning efficiency and teaching effect.

[0175] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering, characterized in that: The steps include: S1. Obtain students’ behavioral and cognitive data during the learning process; S2. Preprocess the collected learning behavior data and cognitive data; S3. Construct a knowledge point map based on the predefined subject knowledge point structure, learning behavior data and cognitive data; S4. Use the polymorphic Bayesian clustering algorithm to construct a dynamic aggregation model of students' thinking paths and initialize the parameters of the dynamic aggregation model of students' thinking paths; S5. Input the preprocessed learning behavior data and cognitive data into the student thinking path dynamic aggregation model, and cluster the student's learning behavior data and cognitive data in real time in combination with the node relationship in the knowledge point map, dynamically capture the changes in the student's thinking path, and generate thinking path tags associated with the knowledge points; S6. Based on the results of dynamic clustering analysis, combined with the learning behavior data and cognitive data of each node in the knowledge point map, calculate the learning mastery of each knowledge point and its thinking jump pattern across knowledge points, and identify the weak links and nonlinear jump logic in the knowledge point association chain of students; S7. Analyze the identified weak links and jumpy thinking paths, optimize students’ learning paths by adjusting the node weights in the knowledge point map and the parameters of dynamic clustering, and form new thinking path aggregation results; S8. Based on the aggregation results of students’ thinking paths after dynamic optimization, generate teaching feedback targeting students’ weak learning links, including recommended supplementary knowledge points, optimized learning sequence and customized learning tasks.

2. According to claim 1, a method for dynamically aggregating student thinking paths based on polymorphic Bayesian clustering is characterized in that: The S1 specifically includes the following sub-steps: S11. Collect students' behavior data during the learning process, including problem-solving steps and problem-solving time information. step represents the sequence of steps that students go through when solving each question, and the problem-solving time information T step It indicates the time students spend solving each operation; S12. Collect students' cognitive data during the learning process, including students' answer accuracy, problem-solving logic structure and knowledge point relevance information, answer accuracy R c It is defined as the ratio of the number of correct answers given by students to the total number of answers given to a specific question or knowledge point. logic Indicates the reasoning path used by students in answering questions, and the knowledge point relevance information A k It indicates the students’ mastery of knowledge point k, which is defined as the proportion of the knowledge point correctly applied in the problem-solving process; S13. Integrate the data obtained from the behavior data collection module and the cognitive data collection module to obtain the behavior data set D1 and the cognitive data set D2: D1={S step ,T step }; D2={R c ,G logic ,A k }。 3. According to claim 1, a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering is characterized in that: The S3 specifically includes the following sub-steps: S31. Define the knowledge point set K = {k1, k2, ..., k m }, where k i represents the i-th knowledge point, based on the learning behavior dataset D1 and the cognitive dataset D2 for each knowledge point k i Constructing feature vectors Eigenvector Including the frequency of students involving knowledge points in the sequence of problem-solving steps The average time students spend solving problems in the problem-solving steps involving knowledge points and students’ mastery of knowledge points S32. Based on students' logical structure of problem solving G logic and knowledge mastery level A k , calculate the knowledge point k i With knowledge point k j The association weight w ij : in, Indicates that students are solving the problem in the logical structure G logic From knowledge point k i To knowledge point k j The number of path occurrences, is the maximum number of path occurrences among all knowledge point pairs, and For students to understand the knowledge point k i and k j The degree of mastery, Represents knowledge point k i and k j The semantic similarity between: in, and are knowledge points k respectively i and k j The characteristic vector of represents the modulus of the feature vector, θ, φ, ψ are the weight coefficients of the association weight, which are used to balance the influence of path frequency, mastery degree and semantic similarity in the calculation of association weight; S33. Constructing knowledge point graph: G knowledge =(K,E,W); Where K is the knowledge point node set, E = {(k i ,k j )|w ij >0,k i ,k j ∈K} is the set of associated edges between knowledge points, indicating that there is an associated relationship between knowledge points. ij ∣(k i ,k j )∈E} is the set of association weights; S34. Calculate each knowledge point k i Importance index The importance index represents the centrality of the knowledge point in the graph: Among them, deg(k i ) is the knowledge point k i The degree of i The number of connected edges, w ij is knowledge point k i With knowledge point k j The weight of the association between .

4. According to claim 1, a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering is characterized in that: The S4 specifically includes the following sub-steps: S41. Constructing a dynamic aggregation model of students' thinking paths based on polymorphic Bayesian clustering algorithm M SP The dynamic aggregation model of students' thinking paths consists of latent variables Z, observed variables X, prior distribution P(Z) and conditional probability distribution P(X|Z), where latent variables represent students' potential thinking path categories, observed variables represent students' behavioral data and cognitive data in the learning process, prior distribution represents the prior probability of the latent category, which is used to initialize the distribution hypothesis of students' thinking path categories, and conditional probability distribution represents the distribution of observed data X under the condition of given latent category Z, which is used to describe the characteristics of data in different categories; S42. Initialize the prior distribution P(Z) and conditional probability distribution P(X|Z) of the dynamic aggregation model of students' thinking paths based on their learning behavior data and cognitive data; S43. Combined with knowledge point graph G knowledge , take the weight W in the knowledge point map as the constraint condition of the dynamic aggregation model of the student's thinking path, and modify the parameters in the conditional probability distribution P(X|Z): Among them, w ij Represents knowledge point k i With k j The association weight, x j is knowledge point k j Observed value of S44. Combine the prior distribution P(Z) and the conditional probability distribution P(X|Z) to calculate the joint probability distribution P(Z,X) of the dynamic aggregation model of student thinking paths: P(Z,X)=P(Z)·P(X|Z).

5. According to claim 1, a method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering is characterized in that: The S5 specifically includes the following sub-steps: S51. Input the preprocessed learning behavior dataset D1 and cognitive dataset D2 into the student thinking path dynamic aggregation model M SP , the input data X is expressed as: X={x1,x2,…,x n },x i ∈D1∪D22: Among them, x i Represents specific observations related to student behavior or cognition; S52. Using the dynamic aggregation model of students' thinking paths M SP Perform real-time clustering on the input data X to generate a latent class label z for each observation i : Where P(Z=z|X=x i ) is calculated by Bayesian inference, combining the prior distribution P(Z) and the conditional probability distribution P(X|Z): Among them, z i Indicates the potential thinking path category of students under the current observation value; S53. Using the knowledge point graph G knowledge The node relationships and weight constraints in ij Correct the clustering result Z and calculate the corrected category distribution P ′ (Z=z|X): Among them, λ is a tuning parameter used to balance the relationship between clustering results and knowledge point graph constraints, neighbor(i) represents the set of nodes adjacent to node i, and δ(z i ,z j ) is the consistency discriminant function, when z i =z j The value is 1 when it is, otherwise it is 0; S54. Generate a student thinking path tag set P associated with the knowledge point based on the modified clustering result Z path , each marker p i Indicates the main thinking path of students in the current time period, according to the knowledge point map G knowledge The path association calculates the path with the largest weight: in, For students in the knowledge point map G knowledge The set of thinking paths in the ij Represents the knowledge point k in the path i and k j The associated weight of .

6. The method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering according to claim 1 is characterized in that: The S6 specifically includes the following sub-steps: S61. Combined with knowledge point graph G knowledge The node attributes and dynamic clustering results Z of the students are calculated for each knowledge point k i Learning mastery in, Representation and knowledge point k i The relevant set of observation data, δ(z j ,z correct ) is the correctness discriminant function, when the clustering result z j It takes the value of 1 when the student has mastered it correctly, otherwise it takes the value of 0. is the same as knowledge point k i The total number of relevant observations, P ′ (Z=z j |X=x j ) represents the modified latent class probability distribution; S62. Using the knowledge point graph G knowledge The edge weight w ij and dynamic clustering result Z to calculate the student's knowledge point k i and k j The thinking jump mode between ij : Among them, H ij Indicates that students learn from knowledge point k i Jump to k j The strength of association, x p and x q are respectively related to knowledge point k i and k j The relevant observation value, E is the set of associated edges in the knowledge point graph; S63. Based on learning mastery and thinking jump mode H ij Identify the weak links in the knowledge point association chain of students and calculate the weak link score S weak : Among them, S weak (k i ,k j ) represents knowledge point k i to k j The weak link score of S weak (k i ,k j ) exceeds a preset threshold, marking the chain as a weak link; S64. Students in the knowledge point map G knowledge The path transfer mode in the nonlinear jump logic probability P is calculated nonlinear : in, Represents a set of expected paths that conform to normal logic. Represents the student's nonlinear jump path.

7. The method for dynamically aggregating students' thinking paths based on polymorphic Bayesian clustering according to claim 1 is characterized in that: The S7 specifically includes the following sub-steps: S71. Locate the weak parts of the associated chains in the knowledge point map based on the identified weak links and the corresponding learning behavior data and cognitive data, including nodes with low mastery of key knowledge points and chains with weaker association weights between nodes; S72. Optimize the association weights of weak links in the knowledge point map based on the weak link analysis results, and increase the connection weights between highly correlated nodes; S73. Update the key parameters of the student thinking path dynamic aggregation model based on the adjusted knowledge point map, and recalculate the observed data distribution and potential category distribution in the student thinking path dynamic aggregation model; S74. Generate an optimized learning path based on the adjusted knowledge point map and the results of the student thinking path dynamic aggregation model, determine the knowledge points that students should focus on in the new learning stage, and mark the learning sequence and jump logic adjustment plan; S75. Store the optimized knowledge point map, student thinking path dynamic aggregation model parameters and learning path aggregation results in the student file management system, and generate a learning path report.

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