Student ability and knowledge point difficulty matching and question recommendation method based on DAG constraint

Abstract

A student ability and knowledge point difficulty matching and question recommendation method based on DAG constraint, comprising: constructing a course DAG knowledge graph; constructing a knowledge point associated question bank; teacher configuring parameters; determining candidate knowledge points and candidate questions; for each question in the candidate question set, the knowledge priority, the student historical error frequency, the ability and the question difficulty matching degree, the review weight based on the forgetting curve are comprehensively weighted to obtain the comprehensive recommendation score; based on the comprehensive recommendation score, the optimization selection with constraint conditions is used to generate the personalized question set of the target student; the feedback of the target student to the personalized question set is obtained, and the error frequency score and the forgetting weight score are updated. The present application realizes efficient management and control of calculation amount and hardware resources, greatly simplifies invalid calculation, reduces CPU, memory and storage I / O load, does not need special high-performance hardware, adapts to medium and low computing power environment and large-scale user scenarios, improves hardware resource utilization, and reduces deployment and operation cost.

Description

Technical Field

[0001] This invention belongs to the field of data analysis and intelligent service technology in the education industry, specifically involving a method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints. Background Technology

[0002] With the advancement of educational informatization, online education platforms and intelligent teaching systems have accumulated massive amounts of course, question bank, and student learning behavior data. While existing learning platforms can provide rich learning resources and pathways, they generally suffer from problems such as fragmented knowledge, chaotic learning paths, high resource selection costs, and homogenized practice content. To address these issues, existing research has utilized knowledge graphs to structure subject knowledge and employed knowledge tracing (KT) technology to characterize students' knowledge states, providing support for personalized recommendations. Related research is gradually developing towards a comprehensive recommendation approach that integrates multiple factors.

[0003] Currently, technical solutions for recommending learning resources, especially question recommendations, mainly fall into three categories: First, question recommendations based on knowledge node relationships or knowledge graphs, such as Chinese patent CN111489602A, entitled "A Question Recommendation Method, Device, and Terminal for a Teaching System." This method automatically generates recommended question data by constructing a knowledge base containing knowledge node relationships and combining it with user-input descriptive information. While this solution utilizes the relationships between knowledge nodes, it only achieves question recommendation based on basic relationships and does not fully consider the prerequisite logical relationships and constraints between knowledge points. Second, Chinese patent CN115687657A, entitled "A Question Recommendation Method Assisted by a Knowledge Graph," first constructs a subject knowledge graph, diagnoses students' current knowledge point mastery through the knowledge graph, and then recommends questions based on question similarity and user similarity characteristics. However, the recommendation logic of this solution still focuses on question retrieval based on similarity, failing to fundamentally solve the core problems of chaotic learning paths and disordered knowledge organization, and lacking effective control over the learnability of prerequisites for recommended questions. Second, there's the recommendation based on matching student ability with question difficulty. Chinese patent CN115329190A, titled "A Question Recommendation Method and System Based on Personalized Ability," extracts knowledge point difficulty features, question difficulty features, and student learning ability features by mining students' historical answer sequences. It then retrieves matching questions from a question bank based on the student's ability status. This approach achieves a preliminary match between ability and difficulty, but it doesn't consider the inherent logical relationships within subject knowledge, easily leading to a disconnect between recommended questions and the knowledge system. Chinese patent CN115827724A, titled "A Test Question Recommendation Method," uses the py-irt model to obtain student ability values ​​and test question difficulty values, then constructs a preference matrix to achieve test question recommendations. However, this approach only focuses on the single dimension of matching ability and difficulty, neglecting key influencing factors such as prior knowledge relationships and student forgetting patterns. The rationality and relevance of the recommendation results still need improvement. Third, there's the learning resource recommendation technology based on forgetting patterns. Chinese patent CN106384319A, entitled "A Personalized Recommendation Method for Teaching Resources Based on the Forgetting Curve," assesses a user's current learning effectiveness and degree of knowledge forgetting based on the Ebbinghaus forgetting curve, and then recommends teaching resources accordingly. While this solution considers the characteristics of students' knowledge forgetting, it does not deeply integrate with factors such as subject knowledge graphs and students' ability status. The types and forms of recommended resources are relatively limited, making it difficult to meet the comprehensive needs of personalized learning.

[0004] Existing question recommendation technologies typically require frequent similarity retrieval, vectorization calculation, and dynamic model updates across the entire question bank. Irregular memory access during graph traversal and multi-hop inference leads to low CPU cache hit rates. Large-scale embedding matrices and real-time graph aggregation calculations result in high memory consumption and heavy storage I / O pressure. The system is highly dependent on high-performance dedicated hardware, making it difficult to deploy stably on educational platforms with low to medium computing power. The high operation and maintenance costs hinder the widespread adoption of personalized recommendation technologies.

[0005] In summary, there is an urgent need for a question recommendation technology that integrates multiple influencing factors and achieves systematic optimization to solve the above problems. Summary of the Invention

[0006] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a method for matching student ability and knowledge point difficulty and recommending questions based on DAG constraints, which has high recommendation accuracy, reduces teachers' teaching workload, and improves the level of teaching intelligence.

[0007] The technical solution adopted to solve the above technical problems is: a method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints, including the following steps:

[0008] Step 1. Construct a course DAG knowledge graph

[0009] Construct a directed acyclic graph G = (V, E) for the course, where V is the set of knowledge points, and V = { }, Let E be the i-th knowledge node, and E be the set of prior relation edges. The prerequisite set is Pre( )={ | ( , )∈E}, express Prerequisite knowledge nodes;

[0010] Step 2. Construct a question bank linking knowledge points

[0011] Build each knowledge node Exclusive question bank , , This is a complete collection of course titles. Each question q in the algorithm is configured with a question type identifier type(q) and a difficulty value H(q) ∈ [0,1].

[0012] Step 3. Teacher Configuration Parameters

[0013] Teachers input the number of questions parameter n, n∈ and the set of knowledge points to be tested ;

[0014] Step 4. Identify candidate knowledge points and candidate questions

[0015] Based on prerequisite relationships and target students' prior knowledge nodes Based on the level of mastery, determine the set of recommended knowledge points. In the set of knowledge points to be examined With the set of recommended knowledge points Construct a set of candidate knowledge points from the intersection of From the complete collection of course titles The candidate question set is obtained by filtering and summarizing the questions associated with the candidate knowledge point set. ;

[0016] Step 5. Analyze the candidate topic set. For each question, a comprehensive recommended score is obtained by comprehensively weighting knowledge priority, student's historical error frequency, the match between ability and question difficulty, and review weight based on the forgetting curve.

[0017] Step 6. Based on the comprehensive recommendation score, use constrained optimization to generate a personalized question set for the target student s. The constraints are as follows:

[0018] Number of questions in the personalized question set ;

[0019] Each knowledge node in the candidate knowledge point set must match at least one question. ;

[0020] For any two questions , If the knowledge points are the same, the question type is the same, and the difference in difficulty is less than the preset threshold, Then the question Choose one of the two;

[0021] Step 7. Obtain feedback from target students on their answers to the personalized question set, and update the error frequency score and forgetting weight score.

[0022] As a preferred technical solution, step 4 involves determining the set of recommended knowledge points. The method is as follows: Set a prerequisite mastery threshold. Define the target student s for knowledge nodes The degree of mastery is If and only if for any prior knowledge node satisfy At that time, knowledge nodes Given a target student *s*, determine the set of recommended knowledge points for *s*. .

[0023] As a preferred technical solution, in step 5, the comprehensive recommendation score is:

[0024]

[0025] In the formula, To determine the overall recommendation score, , , , These are weighted coefficients, all of which are greater than or equal to 0. , Scoring is based on knowledge priority. Scoring students based on their historical error frequency. Scoring is based on the match between ability and question difficulty. The review weight score is based on the forgetting curve.

[0026] As a preferred technical solution, the knowledge priority score , k(q) represents the knowledge points related to question q. and T(k(q)) represents the knowledge point The priority value of the course objective label, corresponding to the weight value of the knowledge point type, L(k(q)) = For knowledge points The priority of the map hierarchy, d( ) is a knowledge point Hierarchical depth in a DAG It represents the maximum depth of the course's knowledge graph.

[0027] As a preferred technical solution, the student historical error frequency score , , Student S represents the knowledge points The number of historical errors, Student S represents the knowledge points The total number of historical answers on the page It is a smoothing term to prevent the denominator from being zero.

[0028] As a preferred technical solution, the ability matching score with the question difficulty is... , , For the target student's ability value, , The difficulty value of the candidate questions. .

[0029] As a preferred technical solution, the review weight score based on the forgetting curve... Review weight score based on forgetting curve The generation method is as follows:

[0030] Step S1. For the target student s, at the knowledge node Maintain the number of repetitions r(s, ), Interval in days I(s, ) and ease factor EF(s, Scoring will be based on the quality of the responses. Update ease factor and to Set a lower bound constraint. ;

[0031] Step S2. Based on the number of repetitions r(s, Corresponding update interval in days ,

[0032]

[0033] Step S3. Obtain the next review time using the following formula. ,

[0034]

[0035] In the formula, This is the time since the last practice session;

[0036] Step S4. Based on the current time With the next review time The forgetting weight score is generated according to the following formula. ,

[0037] .

[0038] As a preferred technical solution, the ease factor The update method is as follows:

[0039]

[0040] In the formula, Grade the quality of student S's answer. .

[0041] The beneficial effects of this invention are as follows:

[0042] This invention, based on the prerequisite relationship constraints and prerequisite knowledge point mastery threshold determination of DAG knowledge graph, only recommends questions related to knowledge points that students already have the prerequisite knowledge base to students. This avoids the problem of recommending questions that are too advanced or skip levels from the outset, which is in line with the students' learning and ability development rules of learning from simple to complex in a step-by-step manner. It effectively reduces students' frustration when answering questions and improves learning efficiency and enthusiasm.

[0043] This invention integrates four core indicators—knowledge priority, student historical error frequency, matching degree between ability and question difficulty, and review weight based on the forgetting curve—to calculate the recommended question score. It focuses on the core knowledge points of the course, accurately identifies students' weak knowledge areas and easily forgotten knowledge points, and achieves a high degree of matching between students' abilities and question difficulty. This allows the recommended questions to accurately meet students' learning needs and truly achieve "teaching according to aptitude."

[0044] This invention ensures the comprehensiveness and diversity of recommended content. It achieves full coverage of the target knowledge points through coverage constraints, and completes the deduplication of questions by combining similarity constraints of knowledge points, question types, and difficulty, avoiding homogeneous exercises and comprehensively improving students' ability to apply knowledge.

[0045] This invention establishes a closed-loop iterative dynamic optimization mechanism, which incrementally updates the error frequency, knowledge mastery, and forgetting curve core parameters based on student feedback, ensuring that recommendations always align with students' latest learning status and continuously improving recommendation effectiveness.

[0046] This invention enhances the intelligence level of teaching and reduces teachers' workload. Teachers only need to complete the basic configuration, and the system can automatically complete the entire recommendation process, solving the problem of the traditional one-size-fits-all approach to topic selection. At the same time, the quantified learning and teaching indicators provide scientific data support for teachers' precise teaching.

[0047] This invention achieves efficient management of computational load and hardware resources. Through pre-screening, modular lightweight computing, and local incremental updates, it significantly reduces ineffective computations, lowers CPU, memory, and storage I / O loads, eliminates the need for dedicated high-performance hardware, adapts to low-to-medium computing power environments and large-scale user scenarios, improves hardware resource utilization, reduces deployment and maintenance costs, and ensures stable and efficient system operation. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the present invention. Detailed Implementation

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0050] exist Figure 1The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints in this embodiment includes the following steps:

[0051] Step 1. Construct a course DAG knowledge graph

[0052] Construct a directed acyclic graph G = (V, E) for the course, where V is the set of knowledge points, and V = { }, Let E be the i-th knowledge node, and E be the set of prior relation edges. The prerequisite set is Pre( )={ | ( , )∈E}, express Prerequisite knowledge nodes;

[0053] Step 2. Construct a question bank linking knowledge points

[0054] Build each knowledge node Exclusive question bank , , This is a complete collection of course titles. Each question q in the algorithm is configured with a question type identifier type(q) and a difficulty value H(q) ∈ [0,1].

[0055] Step 3. Teacher Configuration Parameters

[0056] Teachers input the number of questions parameter n, n∈ and the set of knowledge points to be tested ;

[0057] Step 4. Identify candidate knowledge points and candidate questions

[0058] Based on prerequisite relationships and target students' prior knowledge nodes Based on the level of mastery, determine the set of recommended knowledge points. In the set of knowledge points to be examined With the set of recommended knowledge points Construct a set of candidate knowledge points from the intersection of From the complete collection of course titles The candidate question set is obtained by filtering and summarizing the questions associated with the candidate knowledge point set. ;

[0059] Among them, the set of recommended knowledge points is determined. The method is as follows: Set a prerequisite mastery threshold. Define the target student s for knowledge nodes The degree of mastery is If and only if for any prior knowledge node satisfy At that time, knowledge nodes Given a target student *s*, determine the set of recommended knowledge points for *s*. .

[0060] Step 5. Analyze the candidate topic set. For each question, a comprehensive recommended score is obtained by weighting the following factors: knowledge priority, student's historical error frequency, ability-to-question difficulty match, and review weight based on the forgetting curve:

[0061]

[0062] In the formula, To determine the overall recommendation score, , , , These are weighted coefficients, all of which are greater than or equal to 0. , Scoring is based on knowledge priority. , Scoring students based on their historical error frequency. , Scoring is based on the match between ability and question difficulty. , For review weight scores based on the forgetting curve, ;

[0063] Among them, knowledge priority score k(q) represents the knowledge points related to question q. and T(k(q)) represents the knowledge point The priority value of the course objective label, corresponding to the weight value of the knowledge point type, L(k(q)) = For knowledge points The priority of the map hierarchy, d( ) is a knowledge point Hierarchical depth in a DAG It represents the maximum depth of the course knowledge graph;

[0064] Student History Error Frequency Score , Student S represents the knowledge points The number of historical errors, Student S represents the knowledge points The total number of historical answers on the page It is a smoothing term to prevent the denominator from being zero;

[0065] Ability matching score with question difficulty , For the target student's ability value, , The difficulty value of the candidate questions. ;

[0066] Review weight score based on forgetting curve The generation method is as follows:

[0067] Step S1. For the target student s, at the knowledge node Maintain the number of repetitions r(s, ), Interval in days I(s, ) and ease factor EF(s, Scoring will be based on the quality of the responses. Update the ease factor according to the following formula. and to Set a lower bound constraint. ,

[0068]

[0069] In the formula, ;

[0070] Step S2. Based on the number of repetitions r(s, Corresponding update interval in days ,

[0071]

[0072] Step S3. Obtain the next review time using the following formula. ,

[0073]

[0074] In the formula, This is the time since the last practice session;

[0075] Step S4. Based on the current time With the next review time The forgetting weight score is generated according to the following formula. ,

[0076] .

[0077] Step 6. Based on the comprehensive recommendation score, use constrained optimization to generate a personalized question set for the target student s. The constraints are:

[0078] Number of questions in the personalized question set ;

[0079] Each knowledge node in the candidate knowledge point set must match at least one question. ;

[0080] For any two questions , If the knowledge points are the same, the question type is the same, and the difference in difficulty is less than the preset threshold, Then the question Choose one of the two;

[0081] Step 7. Obtain feedback from target students on their answers to the personalized question set, and update the error frequency score and forgetting weight score.

Claims

1. A method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints, characterized in that, Includes the following steps: Step 1. Construct a course DAG knowledge graph Construct a directed acyclic graph G = (V, E) for the course, where V is the set of knowledge points, and V = { }, Let E be the i-th knowledge node, and E be the set of prior relation edges. The prerequisite set is Pre( )={ | ( , )∈E}, express Prerequisite knowledge nodes; Step 2. Construct a question bank linking knowledge points Build each knowledge node Exclusive question bank , , This is a complete collection of course titles. Each question q in the algorithm is configured with a question type identifier type(q) and a difficulty value H(q) ∈ [0,1]. Step 3. Teacher Configuration Parameters Teacher inputs the number of questions parameter n, n∈ and the set of knowledge points to be tested ; Step 4. Identify candidate knowledge points and candidate questions Based on prerequisite relationships and target students' prior knowledge nodes Based on the level of mastery, determine the set of recommended knowledge points. In the target set of knowledge points With the set of recommended knowledge points Construct a set of candidate knowledge points from the intersection of From the complete collection of course titles The candidate question set is obtained by filtering and summarizing the questions associated with the candidate knowledge point set. ; Step 5. Analyze the candidate topic set. For each question, a comprehensive recommended score is obtained by comprehensively weighting knowledge priority, student's historical error frequency, the match between ability and question difficulty, and review weight based on the forgetting curve. Step 6. Based on the comprehensive recommendation score, use constrained optimization to generate a personalized question set for the target student s. The constraints are as follows: Number of questions in the personalized question set ; Each knowledge node in the candidate knowledge point set must match at least one question. ; For any two questions , If the knowledge points are the same, the question type is the same, and the difference in difficulty is less than the preset threshold, Then the question Choose one of the two; Step 7. Obtain feedback from target students on their answers to the personalized question set, and update the error frequency score and forgetting weight score.

2. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 1, characterized in that, Step 4, which involves determining the set of recommended knowledge points, The method is as follows: Set a prerequisite mastery threshold. Define the target student s for knowledge nodes The degree of mastery is If and only if for any prior knowledge node satisfy At that time, knowledge nodes Given a target student *s*, determine the set of recommended knowledge points for *s*. .

3. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 1, characterized in that, In step 5, the overall recommendation score is: In the formula, To determine the overall recommendation score, , , , These are weighted coefficients, all of which are greater than or equal to 0. , Scoring is based on knowledge priority. Scoring students based on their historical error frequency. Scoring is based on the match between ability and question difficulty. The review weight score is based on the forgetting curve.

4. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 3, characterized in that, The knowledge priority score , k(q) represents the knowledge points related to question q. and T(k(q)) represents the knowledge point The priority value of the course objective label, corresponding to the weight value of the knowledge point type, L(k(q)) = For knowledge points The priority of the map hierarchy, d( ) is a knowledge point Hierarchical depth in a DAG It represents the maximum depth of the course's knowledge graph.

5. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 3, characterized in that, Student historical error frequency score , , Student S represents the knowledge points The number of historical errors, Student S represents the knowledge points The total number of historical answers on the page It is a smoothing term to prevent the denominator from being zero.

6. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 3, characterized in that, The score reflects the match between the ability and the difficulty of the question. , , For the target student's ability value, , The difficulty value of the candidate questions. .

7. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 3, characterized in that, The review weight score based on the forgetting curve Review weight score based on forgetting curve The generation method is as follows: Step S1. For the target student s, at the knowledge node Maintain the number of repetitions r(s, ), Interval in days I(s, ) and ease factor EF(s, Scoring will be based on the quality of the responses. Update ease factor and to Set a lower bound constraint. ; Step S2. Based on the number of repetitions r(s, Corresponding update interval in days , Step S3. Obtain the next review time using the following formula. , In the formula, This is the time since the last practice session; Step S4. Based on the current time With the next review time The forgetting weight score is generated according to the following formula. , 。 8. The method for matching student ability with knowledge point difficulty and recommending questions based on DAG constraints according to claim 7, characterized in that, The ease factor The update method is as follows: In the formula, Grade the quality of student S's answer. .

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