Personalized learning path recommendation method based on course knowledge point sequence

Abstract

The invention belongs to the technical field of intelligent education and personalized learning, and provides a personalized learning path recommendation method based on a course knowledge point sequence. The method aims at solving the problems that existing learning path recommendation logic association is insufficient, the personalized matching degree is low, and the optimization efficiency is not high. The method comprises the following steps: constructing a knowledge point sequence model by adopting a topological sorting algorithm on the basis of a curriculum knowledge point pre-modification and post-modification relationship, a difficulty level and dependence intensity, and generating a structured knowledge relationship graph; a learner feature model and a knowledge resource model are established, learner features are described from the dimensions of learning targets, cognitive levels, learning styles and the like, and the matching degree with knowledge points is calculated; and constructing an optimization model taking learning cost minimization, mastering degree maximization and path continuity optimization as targets, performing iterative optimization by using an improved intelligent optimization algorithm, and generating a learning path with logic rationality and personalized adaptability. According to the method, the scientificity and learning efficiency of learning path recommendation can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent education and personalized learning technology, specifically involving a personalized learning path recommendation method based on the sequence of course knowledge points. Background Technology

[0002] With the rapid development of information technology and artificial intelligence, the digital transformation of education is accelerating, and online education, smart education, and personalized learning have become important development directions in the education field. Compared with traditional offline teaching models, online learning has advantages such as abundant resources, flexible time, and diverse formats, greatly expanding learners' learning space and methods. However, when faced with a vast amount of learning resources, learners often encounter problems such as unclear learning goals, difficulty in resource selection, and chaotic learning paths, resulting in low learning efficiency and a poor learning experience.

[0003] While most online learning platforms currently offer course recommendation functions, these are primarily based on learner interests or behavioral characteristics, lacking in-depth analysis of the logical structure of knowledge content. This makes it difficult to ensure the scientific rigor and systematic nature of the recommended paths. Some researchers have attempted to improve learning path recommendations using methods such as knowledge graphs and learner modeling, but problems remain, including fragmented learning content logic, insufficient personalized matching, and low algorithm optimization efficiency. For example, some recommendation methods based on collaborative filtering or deep learning, while reflecting learner preferences to some extent, often overlook the prerequisite relationships and hierarchical dependencies between knowledge points; and while path construction methods based on knowledge graphs are logically sound, they are insufficient in dynamically adapting to individual learning characteristics.

[0004] Furthermore, existing learning path optimization algorithms mostly focus on the static recommendation stage, lacking dynamic updates and adaptive adjustments to the learning process. This makes it difficult to address changes in learners' learning abilities and differences in knowledge mastery. Consequently, recommended learning paths often fail to adapt to learning progress, impacting learners' sustained learning experience and effectiveness. Therefore, there is an urgent need for a learning path recommendation method that can simultaneously consider the logical connections between knowledge points and learners' individual characteristics, while possessing dynamic optimization capabilities. This would enable the scientific construction and accurate matching of learning paths, thereby improving the intelligence level of personalized learning and the quality of educational services. Summary of the Invention

[0005] This invention addresses the common problems in existing learning path recommendation systems, such as fragmented learning content logic, insufficient personalized matching, and lagging path adjustment. It proposes a personalized learning path recommendation method based on the sequence of course knowledge points. This method achieves an integrated process of logical construction, personalized recommendation, and dynamic optimization of learning paths by systematically modeling the logical relationships between course knowledge points and combining learner feature modeling with intelligent optimization algorithms. This improves the scientific rigor, adaptability, and continuous optimization capabilities of learning recommendations.

[0006] Existing technologies mostly focus on static recommendation of learning resources, lacking systematic analysis of course knowledge structure and the ability to dynamically adjust learning paths based on learners' cognitive levels and learning progress. This results in logical gaps, low adaptability, and poor learning efficiency in the recommendation results. This invention introduces a process framework of "knowledge point serialization modeling - learner feature characterization - resource matching optimization - dynamic feedback adjustment," optimizing the learning path generation mechanism from both the knowledge logic layer and the learning behavior layer, thus constructing an intelligent learning path recommendation method oriented towards individual characteristics.

[0007] The technical solution proposed in this invention includes the following main steps: First, a course knowledge graph is constructed based on the course syllabus, textbooks, and teaching resources. Prerequisite dependencies and hierarchical structures between knowledge points are extracted, and a topological sorting algorithm is used to generate a logically ordered sequence of course knowledge points. Second, learners' basic information, learning characteristics, knowledge mastery status, and learning preferences are collected to construct a multi-dimensional learner model, achieving accurate characterization of individual learner differences. Third, a learning resource model is established for different learner characteristics and knowledge point attributes, and resource suitability is calculated. A multi-objective optimization algorithm is used to comprehensively weigh efficiency, cost, and quality to generate the optimal personalized learning path. Finally, the learning path is dynamically adjusted based on learners' real-time learning progress and feedback data to achieve continuous optimization and personalized adaptation.

[0008] The overall architecture of this invention includes multiple collaborative modules, specifically: a course knowledge point sequence construction module, a learner model construction module, a learning resource model construction module, an intelligent optimization and solution module, a learning path dynamic adjustment module, a path visualization and output module, a course knowledge point sequence management module, a learner model update module, and a learning resource library maintenance module. These modules collaborate with each other through data interfaces, forming a complete closed-loop system from course knowledge modeling to path recommendation and dynamic optimization.

[0009] The course knowledge point sequence construction module realizes the logical modeling of the course knowledge system. Through the extraction of knowledge points, attribute calculation and sequence sorting, it establishes a learning content sequence that conforms to the cognitive laws. The learner model construction module forms an individual profile of learners by characterizing them through multiple dimensions such as identity attributes, learning objectives, learning abilities and knowledge mastery status, providing data support for path matching. The learning resource model construction module takes knowledge points as the core and maps different types of learning resources to knowledge points and learner characteristics to ensure accurate matching of resources and needs.

[0010] The intelligent optimization and solution module, based on intelligent search technologies such as genetic algorithms and particle swarm optimization, transforms the learning path recommendation problem into a multi-objective optimization problem. It achieves a comprehensive balance between learning cost, time efficiency, and knowledge mastery quality, generating the optimal path solution that meets the individual needs of learners. The learning path dynamic adjustment module adaptively corrects the learning path by collecting learning progress, mastery, and learning feedback data in real time, ensuring that the recommendation results continuously match the learner's knowledge status and learning pace.

[0011] The path visualization and output module is responsible for presenting the optimized learning path to learners in an intuitive and structured way. It displays the learning sequence, resource type, learning duration and mastery status through a timeline-style visualization interface, and provides resource access links and learning progress statistics functions to achieve visualized management and efficient execution of the learning process.

[0012] The course knowledge point sequence management module enables versioned storage and updating of knowledge sequences, supporting iterative maintenance of different course versions and knowledge systems; the learner model update module periodically or as needed modifies learner profiles to reflect changes in their learning behavior and ability improvements; and the learning resource library maintenance module ensures the effectiveness, reliability, and richness of recommended resources through quality monitoring, expert review, and diversity supplementation.

[0013] This invention establishes a three-dimensional learning path recommendation system that integrates "logic, individuality, and dynamism" through the synergistic interaction of modules. "Logic" ensures that the path follows the inherent structure and cognitive sequence of the course knowledge; "individuality" guarantees that path recommendations are generated differentiated based on learner characteristics; and "dynamism" enables the system to continuously optimize the path based on real-time data from the learning process, achieving adaptive control of the learning process.

[0014] During implementation, the system first analyzes the knowledge structure of the course, constructs a sequence of knowledge points and identifies prerequisite relationships, and then generates an initial learning path based on the learner profile. Subsequently, the system calculates the comprehensive benefit function of different path schemes through optimization algorithms and selects the optimal path that meets the target constraints. During the learner's execution of the path, the system continuously collects learning data and adjusts subsequent learning nodes and resource combinations in real time based on mastery, learning progress and feedback information, forming a closed-loop optimization mechanism.

[0015] In teaching practice, this invention can support different types of learning scenarios, such as college courses, vocational skills training, and online education platforms. It can flexibly adjust the path recommendation strategy according to the learner's goals (such as "basic mastery", "exam preparation", and "skill expansion"), thereby improving learning efficiency and the quality of knowledge acquisition.

[0016] By applying this invention, the generation of learning paths no longer relies on static rules or single feature matching, but rather on a dynamic generation mechanism based on knowledge logic modeling and individual data-driven approaches, achieving a personalized learning experience of "one path for each person." This method can be widely applied to intelligent education systems, online course platforms, and adaptive learning systems, possessing high scalability and practical application value.

[0017] This invention not only enhances the scientific rigor and intelligence of learning path recommendations but also provides new technological support for the digital transformation of education. By introducing knowledge point serialization modeling and intelligent optimization mechanisms, it achieves end-to-end linkage from curriculum structure to learning behavior, promoting the precision and intelligence of personalized education services.

[0018] In summary, the personalized learning path recommendation method based on course knowledge point sequences provided by this invention can take into account the consistency of knowledge logic, learners' personalized needs, and dynamic adaptability, providing an efficient, reliable, and continuously optimizable technical solution for educational informatization and intelligent learning. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a personalized learning path recommendation method based on a sequence of course knowledge points is provided.

[0020] Figure 2 The diagram shows the knowledge point sequence construction module.

[0021] Figure 3 The diagram shows the learning and learning resource model building blocks.

[0022] Figure 4 A learning path recommendation module diagram is shown. Detailed Implementation

[0023] The invention will now be further described with reference to the accompanying drawings.

[0024] according to Figure 1 The implementation of this invention follows a complete workflow logic of "data input - module collaboration - path generation - dynamic optimization - visualization output," with each core module and supporting module forming a closed loop through data exchange. Course data, learner data, and resource data are preprocessed and then input into the corresponding modeling modules to generate knowledge point sequences, learner models, and learning resource models. These three core results are then fed into the intelligent optimization and solution module to generate an initial path. The dynamic adjustment module then adapts the path to the real-time learning status, and finally, the results are output to the terminal through the visualization module. Simultaneously, the management module handles data storage and iterative maintenance.

[0025] Example 1: Taking the "Data Structures" course in university computer science as an application scenario, and targeting second-year students with "zero prior knowledge, full-time study, and mastery based on learning objectives," the specific implementation process of the personalized learning path recommendation method based on the course knowledge point sequence of this invention is as follows:

[0026] Step 1: Initiate the course knowledge point sequence construction and dual-model building process. The course knowledge point sequence construction module first collects multi-source data, including the course syllabus, classic textbook chapters, teaching materials, and the end-of-chapter exercise sets from the past three years. It then extracts core knowledge points such as "arrays," "linked lists," "stacks," "queues," "trees," and "graphs" as knowledge graph nodes using a combination of manual annotation and the TextRank algorithm. Leveraging expert judgment from computer science lecturers and the Apriori association rule mining algorithm, it accurately identifies logical relationships between knowledge points, such as "prerequisite-successor" and "dependency-support," as graph edges. The complete knowledge graph is then stored in the Neo4j graph database for visualized management and retrieval. Subsequently, each knowledge point node is quantified with multi-dimensional attributes. The difficulty coefficient is calculated based on the test accuracy and actual learning time of historical learners (e.g., "array" 0.2, "graph" 0.8). The importance is obtained according to the proportion of the number of associations between the knowledge point and other knowledge points (e.g., "linked list" 0.086). The centrality is calculated by the "out-degree / in-degree" ratio (e.g., "stack" 2.0). Then, topological sorting is used to ensure the logical order. Combined with the principle of "easy → difficult, high importance → low importance", a second optimization is performed to finally generate the course knowledge point sequence of "array → linked list → stack → queue → tree → search → sort → graph". Simultaneously, learner and learning resource models are constructed. The learner model collects learners' basic attributes (student ID, computer science major, full-time study scenario), learning characteristics (basic mastery of the target knowledge, learning efficiency 0.6, basic level cognition, preference for videos + short, high-frequency content), and knowledge status ("array" knowledge mastered, "linked list" knowledge weak, others to be mastered). The learning resource model matches multiple types of resources for each knowledge point. Taking "linked list" as an example, it matches 25 minutes of teaching videos (fully covered, free, low difficulty, suitability 1.0), 30 minutes of exercise text (partially covered, free, low difficulty, suitability 0.6), and 15 minutes of supplementary animation (supplementary extension, free, low difficulty, suitability 0.9), clarifying the core attributes of resources such as coverage, duration, cost, and suitability.

[0027] Step 2: Proceed to the multi-objective optimization and initial optimal path generation stage. The multi-objective optimization and intelligent solution module first sets three core objective functions: efficiency (minimum total time SRT), cost (minimum total cost SRC), and quality (maximum total score SRQ). These are then transformed into a single objective function RA = α × (1 / SRT) + β × (1 / SRC) + γ × SRQ (where α = 0.3, β = 0.2, γ = 0.5, and α + β + γ = 1) through weighted summation. Using "knowledge points to be mastered + resources with fitness ≥ 0.6" as the basic "genes," 30 initial learning paths are initialized, and the RA value of each path is calculated as its fitness. Iterative optimization is carried out through a genetic algorithm, directly inheriting excellent individuals with RA > 0.4 to the next generation, and selecting 30% of poor individuals using a roulette wheel selection method. Crossover operations (exchanging path segments and verifying logical coherence) are performed with a probability of 0.8, and mutation operations (replacing resources with higher fitness) are performed with a probability of 0.1. After 50 iterations, the optimal initial learning path with RA = 0.52 is selected.

[0028] Step 3: Activate the dynamic adjustment mechanism for the learning path. During the learning process following the initial path, the dynamic adjustment module collects three types of core data in real time: learning progress data (e.g., completion rate of "linked list" videos, deviation between actual and suggested learning time), knowledge mastery data (e.g., scores on "linked list" in-class quizzes, accuracy rate of answering exercises), and feedback data (e.g., resource difficulty evaluation, learning willingness). When the in-class quiz score for a "linked list" knowledge point is only 55 points (<60 points), meeting the "knowledge mastery not up to standard" trigger condition, the system immediately adds a 15-minute animated explanation video and specialized practice questions after the "linked list" knowledge point as supplementary resources, and temporarily suspends subsequent learning of "stack" knowledge points that rely on the "linked list." If subsequent actual learning time exceeds twice the suggested time (judged as "learning difficulty"), or learners actively report resource incompatibility, corresponding adjustment strategies such as splitting learning units and replacing highly compatible resources will be implemented simultaneously to ensure that the learning path always adapts to the learner's real-time knowledge status and ability changes.

[0029] Step 4: Complete the path visualization output and full-process collaborative maintenance. The path visualization and output module presents the optimized learning path in the form of a timeline, clearly marking the estimated learning time, corresponding resource type, priority (labeled as "high / medium / low" based on importance), and learning status ("to be learned", "in progress", "mastered") for each knowledge point. It integrates direct access links to resources and displays the overall learning progress, knowledge mastery rate, and learning efficiency in real time, making it convenient for learners to intuitively understand their own status and efficiently execute their learning plans. Meanwhile, the course knowledge point sequence storage and management module stores the generated knowledge point sequences in JSON format in the database, associated with the course ID, version number, and update time. It supports multi-dimensional queries and iterative updates by course ID, knowledge point name, difficulty, and other dimensions. The learner model update module updates the learner's knowledge status attributes and learning ability attributes based on process data after each learning stage (such as the "array-linked list-stack" unit). If the learning goal or scenario changes, it triggers an immediate update of the learning feature attributes and generates a version snapshot backup for the model. The learning resource library maintenance module ensures the quality of new resource access through a dual mechanism of "expert review + automatic verification." It regularly calculates resource quality scores based on learner evaluations, resource usage rates, and knowledge point test scores, marking resources with scores <0.5 as "needs optimization." At the same time, it supplements diverse resources for knowledge points with a single resource type, ensuring that each knowledge point has at least 2-3 types of compatible resources, forming a complete closed loop for collaborative maintenance throughout the entire process.

[0030] according to Figure 2 The construction of the course knowledge point sequence begins with the collection of learning resources. First, these original course resources are processed to extract a dataset containing knowledge points and their relationships, which is then stored in a CSV file for later retrieval. Next, knowledge point entities and their logical relationships (such as "prerequisite-successor") are extracted from the dataset, and a course knowledge graph is built based on this. The graph is then stored in the Neo4j graph database for visual management. Finally, based on the knowledge graph, a topological sorting algorithm is used to sort the knowledge points according to their dependencies, resulting in a logically coherent knowledge point sequence that conforms to the cognitive order, providing a core framework for subsequent recommended paths.

[0031] Example 2: Taking "Python Automated Operations and Maintenance" vocational skills training as an application scenario, and targeting learners who are "on-the-job IT operations and maintenance personnel, have no prior experience, and whose learning objective is skills application," the specific implementation process of the personalized learning path recommendation method based on the course knowledge point sequence of this invention is as follows:

[0032] Step 1: Initiate the course knowledge point sequence construction and dual-model building process. The course knowledge point sequence construction module collects data from enterprise operation and maintenance textbooks, script case libraries, industry standards, etc., and extracts core knowledge points such as "Python basic syntax" and "paramiko library application" as graph nodes through "manual annotation + TextRank algorithm". With the help of senior operation and maintenance engineers' judgment and Apriori algorithm, the logical relationship of "basic → advanced" and "theory → practice" is mined as edges and stored in the Neo4j database. The knowledge point attributes are quantified: "Python basic syntax" difficulty 0.3, "operation and maintenance script writing" importance 0.9, "paramiko library application" centrality 2.0. After topological sorting and "practicality first" optimization, a knowledge point sequence adapted to the workplace is generated. Simultaneously build two models: The learner model collects features such as on-the-job scenarios, fragmented pace, and preference for practical videos, and marks Python-related knowledge points as to be mastered; the learning resource model matches each knowledge point with short resources of ≤30 minutes, such as matching "paramiko library application" with a 20-minute practical video (fitness 1.0) and a 15-minute script template (fitness 0.9).

[0033] Step 2: Proceed to the multi-objective optimization and initial optimal path generation stage. The multi-objective optimization module sets three main objectives: efficiency (α = 0.5), cost (β = 0.3), and quality (γ = 0.2), which are transformed into a single-objective function RA = α × (1 / SRT) + β × (1 / SRC) + γ × SRQ. Using "knowledge points to be mastered + highly adaptable short-term resources" as the gene, 25 initial paths are initialized. After 40 iterations using a genetic algorithm (crossover probability 0.8, mutation probability 0.1), the optimal initial path with RA = 0.48 is selected.

[0034] Step 3: Activate the dynamic adjustment mechanism for the learning path. During the learner's learning process, the system collects three types of data in real time: progress, mastery level, and feedback. If the learning of "Regular Expressions" stagnates for more than 3 days, an adjustment is triggered: it is split into two 15-minute units, and a review reminder is pushed; after the practical test accuracy rate reaches 65%, 5 industry-scenario practice questions are added. If subsequent issues such as resource incompatibility or difficulty in understanding arise, strategies such as replacing resources and adding practical guidance are implemented simultaneously.

[0035] Step 4: Complete the visual output of the learning path and the collaborative maintenance of the entire process. The visualization module presents the path on a timeline, breaks down the plan into "30-minute daily" segments, marks resource types, priorities, and learning status, integrates resource links and practical entry points, and displays progress and efficiency in real time. The management module stores the sequence and supports updates and queries. The learner model is updated iteratively by unit, and the resource library ensures quality through "expert review + automatic verification," supplementing resources for new workplace scenarios to form a complete closed loop.

[0036] according to Figure 3The core of this module is building adapted learner and learning resource models. For learners, it collects features such as learning objectives (e.g., basic mastery, exam preparation), cognitive level (basic / advanced), learning style (preference for video / text), and available study time to form a learner model that reflects individual differences. For learning resources, it extracts attributes such as knowledge point information, difficulty level (low / medium / high), media type (video / courseware / exercise), and required study time to construct a learning resource model. Finally, through feature matching, it matches learners' needs (e.g., short-term, high-frequency learning) with resource attributes (e.g., videos under 30 minutes), preparing for subsequent accurate recommendations.

[0037] according to Figure 4 The learning path recommendation first clarifies multi-dimensional optimization goals (corresponding to A, B, C, and D in the diagram, such as efficiency, quality, and cost), then uses the weighted formula X = aA + bB + cC + dD to transform the multi-goal into a single goal, while setting constraints for path generation (such as total time and resource type limitations). Next, intelligent algorithms such as ant colony optimization, particle swarm optimization, and genetic algorithms are used to solve the problem, with different algorithms searching for the optimal solution from different perspectives. Finally, a recommendation algorithm evaluates the effectiveness of these solutions, selects the most suitable solution, and ultimately generates the optimal learning path that meets the learner's needs.

[0038] Example 3: Taking after-school tutoring for the "geometry section" of junior high school mathematics as an application scenario, and targeting learners who are "second-year junior high school students with weak foundations and whose learning goals are to improve their exam performance," the specific implementation process of the personalized learning path recommendation method based on the sequence of course knowledge points of this invention is as follows:

[0039] Step 1: Initiate the course knowledge point sequence construction and dual-model building process. The course knowledge point sequence construction module collects geometry chapters from junior high school mathematics textbooks, the high school entrance examination syllabus, and past five years' exam questions. It extracts core knowledge points such as "triangle properties," "congruent triangle criteria," "applications of similar triangles," and "geometric proofs" as graph nodes using "manual annotation + TextRank algorithm." Utilizing the mathematics teacher's criteria and the Apriori algorithm, it mines logical relationships of "theorem → application" and "simple → complex" as edges, storing them in the Neo4j database. Knowledge point attributes are quantified: "triangle properties" has a difficulty level of 0.4, "geometric proofs" has an importance level of 0.9 due to its 20% weighting in the high school entrance examination, and "similar triangles" has a centrality of 1.8. After topological sorting and "exam-focused priority" optimization, a knowledge point sequence adapted to the exam is generated. Simultaneously build two models: The learner model collects information such as after-school tutoring scenarios, basic weaknesses (basic level of cognition), and preferences for text and past exam questions, marking "Properties of Triangles" as a weak knowledge point and the rest as to be mastered; the learning resource model matches suitable resources for each knowledge point, such as matching "Geometric Proofs" with a 45-minute video analysis of past exam questions (fitness 1.0) and a 30-minute tiered practice question (fitness 0.9).

[0040] Step 2: Proceed to the multi-objective optimization and initial optimal path generation stage. The multi-objective optimization module sets three main objectives: efficiency (α = 0.2), cost (β = 0.2), and quality (γ = 0.6, focusing on the adaptability to past exam questions), which are transformed into a single-objective function RA = α × (1 / SRT) + β × (1 / SRC) + γ × SRQ. Using "knowledge points to be mastered + highly adaptable past exam question resources" as the gene, 20 initial paths are initialized. After 35 iterations using a genetic algorithm (crossover probability 0.8, mutation probability 0.1), the optimal initial path with RA = 0.51 is selected.

[0041] Step 3: Activate the dynamic adjustment mechanism for the learning path. During the learner's learning process, the system collects three types of data in real time: practice accuracy, video viewing progress, and feedback on incorrect answers. When the accuracy rate for the "similar triangles" exercise is only 40%, an adjustment is triggered: a 20-minute video explaining the difficult points and two sets of basic practice questions are added; after one week, the accuracy rate is retested and it increases to 70%, restoring the original path progress. If there are delays in progress or unsuitable resource difficulty, strategies such as splitting knowledge points and replacing text and image resources are implemented simultaneously.

[0042] Step 4: Complete the visualized output of the learning path and the collaborative maintenance of the entire process. The visualization module presents the path on a timeline, plans the progress according to "3 lessons per week," marks the star rating of test points, resource types, and mastery status, integrates links to past exam questions and entry points to the error notebook, and displays the score improvement trend in real time. The management module stores the sequence and links it to the syllabus updates. The learner model updates the knowledge status weekly, and the resource library optimizes resources through "teacher review + accuracy analysis," supplementing new question types for the high school entrance examination, forming a complete closed loop.

Claims

1. A personalized learning path recommendation method based on a sequence of course knowledge points, characterized in that, Includes the following steps: S1: Construct a course knowledge graph from the course syllabus, textbooks, and teaching resources. Extract knowledge point entities through manual annotation and the TextRank algorithm. Use the Apriori association rule mining algorithm to identify the prerequisite-successor relationships and hierarchical dependency structures between knowledge points. Store the completed knowledge graph in the Neo4j graph database for visual management and retrieval. S2: Based on the knowledge graph, use a topological sorting algorithm to generate a sequence of course knowledge points that conforms to the cognitive logical order. Quantify the attributes of each knowledge point in multiple dimensions, including a difficulty coefficient calculated based on the weighted average of historical learner test accuracy and actual learning time, an importance calculated based on the proportion of knowledge point associations, and a centrality calculated based on the ratio of out-degree to in-degree. S3: Simultaneously collect learners' identity attributes, learning scenarios, learning goals, cognitive levels, learning efficiency, knowledge mastery status, and learning preferences to construct an individual learner profile model; S4: Establish a learning resource mapping model for each knowledge point, matching various types of learning resources such as videos, texts, exercises, and animations to the knowledge points, and calculating resource coverage, learning duration, cost, difficulty, and a suitability index based on multi-dimensional attributes; S5: Based on the course knowledge point sequence, learner model, and learning resource model, use a genetic algorithm to construct a multi-objective optimization function RA=α×(1 / SRT)+β×(1 / SRC)+γ×SRQ, where SRT is the total learning duration, SRC is the total cost, SRQ is the total quality score, and α, β, and γ are weight coefficients that satisfy α+β+γ=1. Initial personalized learning paths are generated iteratively by initializing the path population, calculating fitness, and selecting crossover and mutation operations; S6: During the learning process, real-time data on learning progress, knowledge acquisition, and feedback are collected to establish a dynamic adjustment mechanism. When it is detected that knowledge acquisition is insufficient, learning progress is lagging behind, or resources are not suitable, adjustment strategies such as adding supplementary resources, splitting learning units, and replacing highly compatible resources are triggered. S7: Through the path visualization and output module, the learning sequence, resource type, learning duration, and mastery status are displayed in the form of a timeline. Resource access links and learning progress statistics are provided to form a complete closed-loop system from knowledge modeling to path recommendation and dynamic optimization.

2. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of constructing the course knowledge graph in step S1 specifically includes: K1: collecting multi-source data such as course outline, classic textbook chapters, teaching materials, and after-class exercises as input; K2: extracting core knowledge points as knowledge graph nodes through manual annotation and TextRank algorithm; K3: accurately identifying the prerequisite-successor and dependency-support logical relationships between knowledge points as graph edges by using domain expert judgment and Apriori association rule mining algorithm; K4: storing the complete knowledge graph in Neo4j graph database to achieve visual management and efficient query.

3. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of generating the course knowledge point sequence in step S2 specifically includes: V1: Generating a basic knowledge point sequence based on the knowledge graph using a topological sorting algorithm; V2: Quantifying the multi-dimensional attributes of each knowledge point, including a difficulty coefficient calculated based on the historical learner test accuracy and actual learning time; V3: Calculating the importance attribute based on the proportion of associations between the knowledge point and other knowledge points; V4: Calculating the centrality attribute based on the ratio of out-degree to in-degree; V5: Performing secondary optimization on the sequence according to the cognitive rules of easy to difficult and high importance to low importance, finally generating a knowledge point learning sequence that conforms to teaching logic and cognitive rules.

4. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of constructing the learner individual profile model in step S3 specifically includes: N1: collecting the learner's basic identity attributes, including academic level, major, and learning scenario information; N2: collecting learning goal attributes, including specific needs for basic mastery, exam preparation, or skill expansion; N3: collecting learning ability attributes, including learning efficiency values ​​and cognitive level; N4: collecting knowledge mastery status attributes, including markers of mastery, weakness, or unmastered status for each knowledge point; N5: collecting learning preference attributes, including the degree of preference for resource types and adaptation mode of learning pace; N6: constructing the learner individual profile based on the collected multi-dimensional features and establishing a regular update mechanism.

5. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of establishing a learning resource mapping model in step S4 specifically includes: F1: Organizing learning resources around knowledge points and matching multiple types of learning resources for each knowledge point; F2: Calculating multi-dimensional attributes for each resource, including the resource's coverage of knowledge points, estimated learning time, acquisition cost, and difficulty level; F3: Calculating the fit index between resources and knowledge points and learner characteristics; F4: Establishing a learning resource library maintenance mechanism, ensuring the quality of new resource access through a dual mechanism of expert review and automatic verification; F5: Regularly calculating resource quality scores, marking low-quality resources as needing optimization, and supplementing with diversified resources.

6. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of generating the initial personalized learning path using a genetic algorithm in step S5 specifically includes: T1: Initializing an initial population containing multiple candidate paths using a combination of knowledge points to be mastered and learning resources with a fitness level not lower than a threshold as the basic genes; T2: Constructing a multi-objective optimization function RA = α × (1 / SRT) + β × (1 / SRC) + γ × SRQ; T3: Calculating the RA value of each path as a fitness evaluation index; T4: Retaining individuals with higher fitness using a roulette wheel selection method; T5: Performing a crossover operation with a set crossover probability, exchanging fragments of different paths and verifying the logical coherence of knowledge points; T6: Performing a mutation operation with a set mutation probability, replacing resources in the path with resources of higher fitness; T7: Through multiple generations of iterative evolution, finally selecting the path with the highest fitness as the optimal personalized learning path scheme.

7. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of establishing a dynamic adjustment mechanism in step S6 specifically includes: Q1: Establishing a learning process monitoring mechanism to collect three types of core data in real time; Q2: Setting multi-dimensional trigger conditions, including insufficient knowledge mastery, abnormal learning progress, and insufficient resource adaptation; Q3: Executing corresponding strategies after triggering the adjustment mechanism, including adding supplementary resources, splitting learning units, and replacing resources with higher adaptation; Q4: Forming a closed-loop optimization mechanism of monitoring-evaluation-adjustment to ensure dynamic adaptation of the learning path.

8. The personalized learning path recommendation method based on the sequence of course knowledge points as described in claim 1, characterized in that, The process of visualizing the learning path in step S7 specifically includes: H1: The optimized learning path is displayed in a structured timeline format through the path visualization and output module; H2: The estimated learning time, corresponding resource type, priority identifier, and real-time learning status marker for each knowledge point are clearly marked; H3: Direct access links to resources are integrated, allowing learners to jump to the corresponding learning resources with one click; H4: Learning progress statistics are provided, displaying the overall learning progress percentage, knowledge point mastery rate distribution, and learning efficiency trend analysis in real time; H5: Visual management of the learning process is supported, enabling full lifecycle visual management and efficient execution support for the learning path.

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