Mathematics companion online learning system and method thereof

Abstract

The invention discloses a mathematics accompanying online learning system and a method thereof, and belongs to the technical field of online education. Aiming at the technical bottlenecks of high course development threshold, insufficient interactivity, low individuation degree and weak family-school coordination of the existing mathematics learning platform, the system constructs a dynamic course management-embedded mathematics experiment-intelligent learning engine-family-school coordination monitoring four-layer architecture. Through supporting HTML / JS / CSS interactive course packet low-threshold uploading and real-time rendering, GeoGebrar / network drawing board and other mathematical experiment tools are integrated, AI algorithm is combined to analyze learning behavior data and dynamically plan a personalized path, and a data visual chemical condition monitoring system is synchronously established. According to the invention, a teaching mode of'learning while practicing 'and'learning from middle school' is realized, the course development cost of teachers is reduced, the understanding depth of mathematics abstract concepts of students is improved, a teaching closed loop is strengthened through a family-school cooperation mechanism, and an intelligent, interactive and personalized solution is provided for mathematics online education.

Description

Technical Field

[0001] This invention relates to the field of online education, specifically to an online learning system and method for mathematics learning companions. Background Technology

[0002] With the rapid advancement of educational informatization, online mathematics learning platforms have become an important supplement to traditional teaching. Currently, mainstream mathematics learning platforms on the market (such as "Yuanfudao" and "Zuoyebang") mainly adopt a "video course + standardized question bank" model, supporting teachers to assign homework online, students to complete exercises, and basic data statistics. However, these platforms suffer from significant technical bottlenecks: First, the course development threshold is high. Most existing platform courses are static resources (videos, PDFs), and teachers need to rely on professional technical teams to develop interactive content, resulting in long course update cycles, difficulty in personalization adaptation, and difficulty in meeting diverse teaching needs.

[0003] Secondly, there is a lack of interactivity and experimental support. Abstract concepts in mathematics, such as geometric figures and functional relationships, need to be deepened through practical operations. However, existing platforms lack embedded mathematical experimental tools, and students can only passively receive audiovisual information, unable to adjust parameters or observe changes in real time, resulting in an incomplete understanding of concepts.

[0004] Third, the learning model is monotonous and rigid. A fixed process of learning first and then practicing is commonly used, resulting in a disconnect between course content and practice. Students struggle to consolidate knowledge during the learning process, leading to insufficient learning initiative.

[0005] Fourth, data utilization and home-school collaboration are weak. Learning behavior data has not been fully explored, making it difficult to achieve accurate and personalized recommendations; at the same time, there is a lack of transparent learning progress display and convenient intervention mechanisms, making it impossible for teachers and parents to keep abreast of students' learning dynamics, resulting in poor teaching collaboration.

[0006] To address the aforementioned issues, there is an urgent need to develop an online learning system that supports the development of low-threshold interactive courses, integrates mathematical experimental tools, and features intelligent personalized recommendations and home-school collaboration capabilities, thereby promoting the transformation of online mathematics education from passive reception to active inquiry. Summary of the Invention

[0007] The purpose of this invention is to provide an online learning system and method for mathematics learning companions to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: an online learning system for mathematics learning companions, comprising a dynamic course management module, a mathematics experiment integration module, an intelligent learning engine, and a home-school collaborative monitoring module: the dynamic course management module is used to realize the low-threshold construction, uploading, management, and publishing of interactive mathematics courses, supports teachers to upload interactive course packages (including Storyline output course packages) containing HTML, CSS, and JS files, embeds various teaching resources and test questions, supports course metadata annotation, associates with a large model to realize the analysis of weak knowledge points and push learning suggestions, and provides a split-screen synchronous display function to realize the synchronous conduct of course learning and experiments / exercises, providing basic content guarantee for interactive learning; The integrated mathematical experiment module provides students with an embedded mathematical experiment environment. It has a built-in lightweight GeoGebra / network drawing board engine, supports the direct embedding of experimental components on course pages, provides a mathematical experiment template library covering the K-12 stage, and also supports teachers to upload custom experimental files. Students can operate and adjust mathematical model parameters in real time, observe changes in mathematical laws, and the experimental operation is linked to course knowledge points in real time, strengthening the closed loop of experimental operation-theoretical understanding-practice consolidation, and helping students understand abstract mathematical concepts. The intelligent learning engine is used to realize personalized learning push and real-time Q&A. It collects student learning behavior data in real time (clicks, dwell time, experimental operation trajectory, test results, etc.), builds a learning ability assessment model based on knowledge graph and machine learning algorithm, calculates the learning priority of knowledge points, dynamically plans personalized learning paths, and has a built-in real-time Q&A engine to support system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The intelligent learning engine is used to realize personalized learning push and real-time Q&A. It collects student learning behavior data in real time (clicks, dwell time, experimental operation trajectory, test results, etc.), builds a learning ability assessment model based on knowledge graph and machine learning algorithm, calculates the learning priority of knowledge points, dynamically plans personalized learning paths, and has a built-in real-time Q&A engine to support system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The home-school collaborative monitoring module is used to realize teaching collaboration and closed-loop management among teachers, students and parents. It provides a visual display of learning data, which intuitively presents data including but not limited to students' learning time, answer accuracy, and mastery of knowledge points. It supports teachers to push learning suggestions, supplementary resources and targeted exercises with one click, and allows parents to view students' learning progress and weaknesses in real time. It opens up communication channels among the three parties and realizes data-driven precise teaching intervention.

[0009] Preferably, the specific implementation logic of the mathematical experiment integration module is as follows: Step 1: Initialize and deploy the experimental engine to build the embedded basic environment: The mathematical experiment integrated module pre-integrates the lightweight GeoGebra engine and the network drawing board engine, completes the compatibility adaptation between the engine and the system front end, ensures that students do not need to download and install additional plugins, and directly embeds the interactive course page published by the dynamic course management module. At the same time, it configures the experimental operation response mechanism to ensure that the response time for adjusting experimental parameters and refreshing images is ≤100ms, adapts to the display and operation requirements of multiple terminals such as Windows, iOS and Android, and achieves seamless integration with the course split-screen mode; Step 2: Experiment Template Library Construction and Custom Experiment Upload Adaptation: First, the system pre-builds an experiment template library covering all math knowledge points across K-12 levels, categorized by elementary geometry, middle school functions, and high school statistics and analytic geometry. Examples include triangle congruence verification in elementary school, quadratic function graph transformations in middle school, and probability simulation experiments in high school. Each template is associated with a corresponding knowledge point tag for easy selection by teachers. Second, a custom experiment upload interface is developed, supporting teachers to upload custom experiment files in .ggb format. After uploading, the system automatically parses the experiment parameters and knowledge point association information, matching them with course metadata to ensure accurate correspondence between experiment content and course knowledge points. Step 3: Embedding and Binding Experiment Components with Course Content: When teachers publish interactive courses through the dynamic course management module, they can select the corresponding experiment template from the experiment template library or upload a custom experiment file on the course editing page. The experiment components are then embedded into the corresponding knowledge point chapters of the course. At the same time, the linkage rules between experiments and courses are set—combined with the course split-screen display function, the experiment components are deployed on the right side of the course page and synchronized with the course content on the left side. This ensures that students can immediately carry out experimental operations when they learn the corresponding knowledge points, realizing learning by doing. This step is also linked to the course metadata annotation function of the dynamic course management module, so that the experiment components and course knowledge points form a one-to-one correspondence, laying the foundation for the subsequent correlation and collection of experiment data and knowledge point mastery. Step 4: Student-side interactive experiment operation, real-time presentation of mathematical patterns: When students log into the system to learn the corresponding course, they enter a split-screen learning interface. On the left, they view the course explanation content, and on the right, they click to start the experiment component to conduct real-time operations: They can adjust the parameters of the mathematical experiment model, such as adjusting the quadratic function, by dragging, inputting parameters, clicking to trigger, etc. middle The experimental components render the changes in mathematical laws brought about by parameter changes in real time, such as the selection of values ​​and dragging the vertices of geometric figures to change their shape. The experimental operation steps are displayed synchronously, which makes it easy for students to review the operation process and summarize mathematical laws. The course explanation and playback are not interrupted during the operation, so as to realize the synchronous progress of learning and experimentation. Step 5: Experimental Data Collection and Knowledge Point Consolidation: After students complete the experimental operation, the experimental integration module automatically collects experimental operation data (including operation steps, parameter adjustment records, experiment completion rate, number of erroneous operations, etc.) and pushes it to the intelligent learning engine in real time for subsequent knowledge point mastery assessment and personalized learning path planning. At the same time, the system automatically triggers the linkage mechanism to push consolidation exercises for corresponding knowledge points based on the students' experimental completion status. The exercises focus on the mathematical laws verified by the experiment, strengthening the closed loop of experimental operation-theoretical understanding-practice consolidation. For example, after students complete the quadratic function graph transformation experiment, exercises on judging the influence of parameters on the graph are automatically pushed, realizing a deep binding between experiment and knowledge consolidation. Step 6: Experiment Operation Feedback and Optimization: During the experiment, the mathematics experiment integration module monitors the experimental operation status. If students make mistakes such as incorrect parameter input or unreasonable operation steps, the experimental component will automatically pop up a concise prompt (without interfering with course learning and experimental operation) to guide students to correct their operation. At the same time, the experiment integration module regularly summarizes student experimental operation data and teacher feedback, optimizes the ease of operation of experimental templates, and updates the compatibility of experimental components to ensure that the experimental content, course knowledge points, and personalized recommendations of the intelligent learning engine work together to truly leverage the auxiliary role of practical operation in understanding abstract mathematical concepts.

[0010] Preferably, the intelligent learning engine is implemented using the following steps: Step S1: Engine Initialization and Basic Configuration, Building an Intelligent Support Environment: The intelligent learning engine pre-deploys the core program of the intelligent learning engine, completes interface adaptation with the dynamic course management module, the mathematics experiment integration module, and the home-school collaborative monitoring module, configures the data collection frequency, algorithm parameter thresholds, and large model call interface (connecting to DeepSeek or Doubao AI); at the same time, it imports the K12 stage mathematics knowledge graph, builds an association network according to the grade level and knowledge point level, marks the difficulty coefficient of each knowledge point, related knowledge points and corresponding courses and experimental resources, initializes the learning ability assessment model parameters, and ensures that the engine can receive and process various types of data normally, with a response time of ≤2 seconds, and adapts to multi-terminal usage scenarios; Step S2: Real-time collection and integration of multi-dimensional learning behavior data: The intelligent learning engine collects learning behavior data from multiple sources in real time through preset interfaces to form a complete profile of student learning behavior. Step S3: Calculate the learning ability assessment model to determine the mastery of knowledge points and learning priority. Based on the collected structured data, a pre-set learning ability assessment model is invoked, according to the formula. Perform the calculation, where For the first Learning priorities for each knowledge point For the first The weights for behavioral data are as follows: 0.4 for correct answer rate, 0.3 for experimental operation completion rate, and 0.3 for dwell time. For the first The knowledge point corresponds to the first Standardized score of class behavior, range of values Simultaneously, by combining knowledge graphs, we analyze students' weaknesses in mastering various knowledge points, mark weak knowledge points and related knowledge points, generate preliminary learning ability assessment results, and provide data support for personalized learning path planning. Step S4: Dynamic Planning and Resource Push for Personalized Learning Paths: Based on the learning ability assessment results, combined with the student's grade level and learning progress, a personalized learning path is dynamically planned: For knowledge points with a mastery level ≥ 80%, extended resources (advanced practice questions, extended experiments) are pushed; for knowledge points with a mastery level between 60% and 80%, consolidation resources (basic practice questions, micro-lessons reviewing knowledge points) are pushed; for knowledge points with a mastery level < 60%, basic explanation resources (core micro-lessons, simplified experiment templates) are pushed first, followed by targeted exercises, ensuring that the path matches the student's ability level; all pushed resources come from the course library of the dynamic course management module and the experiment library of the mathematics experiment integration module, while also calling the large model to generate personalized learning suggestions (including learning methods and time allocation guidance) for each learning path, which are pushed to the student's end in real time; Step S5, Real-time Q&A Engine Activation and Multi-mode Q&A Response: When students raise questions during the learning process (course learning, experimental operation, practice and consolidation stage), the real-time Q&A engine is activated, and the response follows the logic of "system matching - large model retrieval - manual backup". Step S6, Synchronization of Learning Data and Dynamic Path Optimization: The intelligent learning engine will synchronize core learning data, including but not limited to student learning ability assessment results, personalized path execution status, and knowledge point mastery, to the home-school collaborative monitoring module in real time, providing data support for the visualization of learning progress and tripartite collaborative intervention. At the same time, it will regularly (every day at midnight) summarize student learning data, update the parameters of the learning ability assessment model, optimize the weight of learning priority calculation, and dynamically adjust personalized learning paths based on student path execution status, Q&A feedback, and test results. For example, if a student's mastery of a weak knowledge point improves to over 80% after intensive learning, the path will be adjusted in a timely manner, and extended resources will be pushed. If a knowledge point still fails to meet the standard after multiple reinforcements, the frequency of basic resource pushes will be increased, and teacher intervention reminders will be pushed simultaneously, forming a closed loop of "data collection-assessment-push-optimization".

[0011] Preferably, the specific content and sources of the multi-source learning behavior data collected in step S2 include: first, course learning data pushed by the dynamic course management module (course click trajectory, dwell time on key content, course completion rate, test answer results and time consumption); second, experimental operation data pushed by the mathematics experiment integration module (operation steps, parameter adjustment records, experiment completion rate, number of erroneous operations, experiment time consumption); and third, student-side active operation data (Q&A content, supplementary resource viewing records, personalized path execution status). After collection, the data is initially cleaned to remove invalid data (such as accidental clicks or abnormal records caused by network interruption), and classified and archived according to student ID-knowledge point-collection timestamp to form a structured data set.

[0012] Preferably, the logical response of "system matching - large model retrieval - manual backup" in step S5 is as follows: First, the system performs resource matching, searching for relevant courses, experiments, and exercises in the dynamic course management module and the integrated mathematics experiment module, and pushing the most relevant resources to the student's question. Second, it searches for answers online; if no matching resources are found in the system, it calls DeepSeek or Doubao AI's large-scale model to retrieve accurate answers and problem-solving strategies, and synchronously associates them with corresponding knowledge points. Next, it recommends related knowledge points, pushing explanations of relevant knowledge points based on the question content to help students apply their knowledge to other situations. Finally, it provides online human Q&A; if students are not satisfied with the AI ​​Q&A results, they can request human Q&A, and the engine will push the question to the corresponding teacher's end, synchronously displaying the student's relevant learning data (mastery of the questioned knowledge points, relevant experiment / exercise status), facilitating accurate Q&A by teachers, and the Q&A record is automatically archived in the student's learning file.

[0013] Preferably, an online learning method for mathematics tutors, applied to an online learning system for mathematics tutors, is characterized by including the following steps: Step 1, Course Construction and Release: Teachers upload interactive course packages through the dynamic course management module, annotate metadata (knowledge points, grade, difficulty), embed mathematical experiment components and test questions, generate structured courses, and release them to the system; Step 2, Interactive Learning Process: Students log in to the system, select the corresponding course, and simultaneously learn and conduct experiments in split-screen mode. After completing the learning of each knowledge point, they immediately complete the targeted exercises pushed by the system, realizing learning and practice at the same time. Step 3, Data Collection and Personalized Recommendation: The intelligent learning engine collects students' learning behavior data in real time, calculates the mastery of knowledge points through the evaluation model, calls the large model to generate learning reports and personalized learning paths, and pushes supplementary resources or reinforcement exercises for weak knowledge points. Step 4: Home-School Collaborative Intervention: The home-school collaborative monitoring module synchronizes learning data, teachers adjust teaching strategies according to the class's learning situation, parents track students' learning progress, and the three parties work together to complete learning intervention, forming a closed loop in teaching.

[0014] Compared with the prior art, the beneficial effects of the present invention are: Lowering the barrier to course development and enhancing teaching flexibility: This invention supports teachers in independently uploading interactive course packages without requiring professional programming skills, is compatible with mainstream course production tools, significantly shortens the course update cycle, and meets personalized teaching needs.

[0015] Enhanced interaction and experimental experience, deepening conceptual understanding: This invention's embedded mathematical experimental tool and split-screen synchronization function allow students to observe mathematical patterns and verify theoretical knowledge during operation, effectively solving the problem of understanding abstract concepts and improving learning initiative and depth.

[0016] Personalized and precise teaching to improve learning efficiency: This invention is based on multi-dimensional behavioral data and AI algorithms to realize personalized learning path planning and real-time feedback, avoiding one-size-fits-all teaching and allowing each student to obtain a learning plan that suits their own abilities, thereby improving the efficiency of knowledge acquisition.

[0017] Improving the home-school collaboration mechanism and optimizing the teaching loop: This invention's transparent learning visualization and convenient intervention functions open up communication channels among teachers, students, and parents, enabling timely identification and resolution of learning problems and strengthening the effectiveness of teaching collaboration. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the system structure of the present invention; Figure 2 This is a schematic diagram of the workflow of the mathematical experiment integration module of the present invention; Figure 3 This is a schematic diagram of the intelligent learning engine workflow of the present invention; Figure 4 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

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

[0020] Please see Figure 1-4This invention provides a technical solution: an online learning system for mathematics learning companions, including a dynamic course management module, a mathematics experiment integration module, an intelligent learning engine, and a home-school collaborative monitoring module. The dynamic course management module is used to realize the low-threshold construction, uploading, management, and publishing of interactive mathematics courses. It supports teachers to upload interactive course packages (including Storyline output course packages) containing HTML, CSS, and JS files, embedding various teaching resources and test questions, supporting course metadata annotation, associating with a large model to realize the analysis of weak knowledge points and push learning suggestions, and providing a split-screen synchronous display function to realize the synchronous conduct of course learning and experiments / exercises, providing basic content guarantee for interactive learning. The integrated math experiment module provides students with an embedded math experiment environment. It features a built-in lightweight GeoGebra / network drawing board engine, supports embedding experiment components directly into course pages, provides a math experiment template library covering the K-12 stage, and allows teachers to upload custom experiment files. Students can adjust mathematical model parameters in real time, observe changes in mathematical patterns, and the experimental operations are linked to course knowledge points in real time, strengthening the closed loop of experimental operation-theoretical understanding-practice consolidation and helping students understand abstract mathematical concepts. The intelligent learning engine is used to realize personalized learning push and real-time Q&A. It collects students' learning behavior data in real time (clicks, dwell time, experimental operation trajectory, test results, etc.), builds a learning ability assessment model based on knowledge graph and machine learning algorithm, calculates the learning priority of knowledge points, and dynamically plans personalized learning paths. At the same time, it has a built-in real-time Q&A engine that supports system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The intelligent learning engine is used to realize personalized learning push and real-time Q&A. It collects students' learning behavior data in real time (clicks, dwell time, experimental operation trajectory, test results, etc.), builds a learning ability assessment model based on knowledge graph and machine learning algorithm, calculates the learning priority of knowledge points, and dynamically plans personalized learning paths. At the same time, it has a built-in real-time Q&A engine that supports system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The home-school collaboration monitoring module is used to realize teaching collaboration and closed-loop management among teachers, students and parents. It provides a visual display of learning data, which intuitively presents data including but not limited to students' learning time, answer accuracy, and mastery of knowledge points. It supports teachers to push learning suggestions, supplementary resources and targeted exercises with one click, and allows parents to view students' learning progress and weaknesses in real time. It opens up communication channels among the three parties and realizes data-driven precise teaching intervention.

[0021] Furthermore, the specific implementation logic of the mathematical experiment integration module is as follows: Step 1: Initialize and deploy the experimental engine to build the embedded basic environment: The mathematical experiment integrated module pre-integrates the lightweight GeoGebra engine and the network drawing board engine, completes the compatibility adaptation between the engine and the system front end, ensures that students do not need to download and install additional plugins, and directly embeds the interactive course page published by the dynamic course management module. At the same time, it configures the experimental operation response mechanism to ensure that the response time for adjusting experimental parameters and refreshing images is ≤100ms, adapts to the display and operation requirements of multiple terminals such as Windows, iOS and Android, and achieves seamless integration with the course split-screen mode; Step 2: Experiment Template Library Construction and Custom Experiment Upload Adaptation: First, the system pre-builds an experiment template library covering all math knowledge points across K-12 levels, categorized by elementary geometry, middle school functions, and high school statistics and analytic geometry. Examples include triangle congruence verification in elementary school, quadratic function graph transformations in middle school, and probability simulation experiments in high school. Each template is associated with a corresponding knowledge point tag for easy selection by teachers. Second, a custom experiment upload interface is developed, supporting teachers to upload custom experiment files in .ggb format. After uploading, the system automatically parses the experiment parameters and knowledge point association information, matching them with course metadata to ensure accurate correspondence between experiment content and course knowledge points. Step 3: Embedding and Binding Experiment Components with Course Content: When teachers publish interactive courses through the dynamic course management module, they can select the corresponding experiment template from the experiment template library or upload a custom experiment file on the course editing page. The experiment components are then embedded into the corresponding knowledge point chapters of the course. At the same time, the linkage rules between experiments and courses are set—combined with the course split-screen display function, the experiment components are deployed on the right side of the course page and synchronized with the course content on the left side. This ensures that students can immediately carry out experimental operations when they learn the corresponding knowledge points, realizing learning by doing. This step is also linked to the course metadata annotation function of the dynamic course management module, so that the experiment components and course knowledge points form a one-to-one correspondence, laying the foundation for the subsequent correlation and collection of experiment data and knowledge point mastery. Step 4: Student-side interactive experiment operation, real-time presentation of mathematical patterns: When students log into the system to learn the corresponding course, they enter a split-screen learning interface. On the left, they view the course explanation content, and on the right, they click to start the experiment component to conduct real-time operations: They can adjust the parameters of the mathematical experiment model, such as adjusting the quadratic function, by dragging, inputting parameters, clicking to trigger, etc. middle The experimental components render the changes in mathematical laws brought about by parameter changes in real time, such as the selection of values ​​and dragging the vertices of geometric figures to change their shape. The experimental operation steps are displayed synchronously, which makes it easy for students to review the operation process and summarize mathematical laws. The course explanation and playback are not interrupted during the operation, so as to realize the synchronous progress of learning and experimentation. Step 5: Experimental Data Collection and Knowledge Point Consolidation: After students complete the experimental operation, the experimental integration module automatically collects experimental operation data (including operation steps, parameter adjustment records, experiment completion rate, number of erroneous operations, etc.) and pushes it to the intelligent learning engine in real time for subsequent knowledge point mastery assessment and personalized learning path planning. At the same time, the system automatically triggers the linkage mechanism to push consolidation exercises for corresponding knowledge points based on the students' experimental completion status. The exercises focus on the mathematical laws verified by the experiment, strengthening the closed loop of experimental operation-theoretical understanding-practice consolidation. For example, after students complete the quadratic function graph transformation experiment, exercises on judging the influence of parameters on the graph are automatically pushed, realizing a deep binding between experiment and knowledge consolidation. Step 6: Experiment Operation Feedback and Optimization: During the experiment, the mathematics experiment integration module monitors the experimental operation status. If students make mistakes such as incorrect parameter input or unreasonable operation steps, the experimental component will automatically pop up a concise prompt (without interfering with course learning and experimental operation) to guide students to correct their operation. At the same time, the experiment integration module regularly summarizes student experimental operation data and teacher feedback, optimizes the ease of operation of experimental templates, and updates the compatibility of experimental components to ensure that the experimental content, course knowledge points, and personalized recommendations of the intelligent learning engine work together to truly leverage the auxiliary role of practical operation in understanding abstract mathematical concepts.

[0022] Furthermore, the specific implementation steps of the intelligent learning engine are as follows: Step S1: Engine Initialization and Basic Configuration, Building an Intelligent Support Environment: The intelligent learning engine pre-deploys the core program of the intelligent learning engine, completes interface adaptation with the dynamic course management module, the mathematics experiment integration module, and the home-school collaborative monitoring module, configures the data collection frequency, algorithm parameter thresholds, and large model call interface (connecting to DeepSeek or Doubao AI); at the same time, it imports the K12 stage mathematics knowledge graph, builds an association network according to the grade level and knowledge point level, marks the difficulty coefficient of each knowledge point, related knowledge points and corresponding courses and experimental resources, initializes the learning ability assessment model parameters, and ensures that the engine can receive and process various types of data normally, with a response time of ≤2 seconds, and adapts to multi-terminal usage scenarios; Step S2: Real-time collection and integration of multi-dimensional learning behavior data: The intelligent learning engine collects learning behavior data from multiple sources in real time through preset interfaces to form a complete profile of student learning behavior. Step S3: Calculate the learning ability assessment model to determine the mastery of knowledge points and learning priority. Based on the collected structured data, a pre-set learning ability assessment model is invoked, according to the formula. Perform the calculation, where For the first Learning priorities for each knowledge point For the first The weights for behavioral data are as follows: 0.4 for correct answer rate, 0.3 for experimental operation completion rate, and 0.3 for dwell time. For the first The knowledge point corresponds to the first Standardized score of class behavior, range of values Simultaneously, by combining knowledge graphs, we analyze students' weaknesses in mastering various knowledge points, mark weak knowledge points and related knowledge points, generate preliminary learning ability assessment results, and provide data support for personalized learning path planning. Step S4: Dynamic Planning and Resource Push for Personalized Learning Paths: Based on the learning ability assessment results, combined with the student's grade level and learning progress, a personalized learning path is dynamically planned: For knowledge points with a mastery level ≥ 80%, extended resources (advanced practice questions, extended experiments) are pushed; for knowledge points with a mastery level between 60% and 80%, consolidation resources (basic practice questions, micro-lessons reviewing knowledge points) are pushed; for knowledge points with a mastery level < 60%, basic explanation resources (core micro-lessons, simplified experiment templates) are pushed first, followed by targeted exercises, ensuring that the path matches the student's ability level; all pushed resources come from the course library of the dynamic course management module and the experiment library of the mathematics experiment integration module, while also calling the large model to generate personalized learning suggestions (including learning methods and time allocation guidance) for each learning path, which are pushed to the student's end in real time; Step S5: Real-time Q&A Engine Activation and Multi-mode Q&A Response: When students raise questions during the learning process (course learning, experimental operation, and practice consolidation stages), the real-time Q&A engine is activated, responding according to the logic of "system matching - large model retrieval - manual backup," specifically as follows: First, system resource matching: retrieving related courses, experiments, and exercises from the dynamic course management module and the mathematics experiment integration module, and pushing the most relevant resources to the question; Second, online Q&A retrieval: if no matching resources are found in the system, calling DeepSeek or Doubao AI large model to retrieve accurate answers and problem-solving strategies, and synchronously associating corresponding knowledge points; Third, knowledge point association recommendation: combining the question content, pushing relevant knowledge point explanation resources to help students apply what they have learned to other situations; Fourth, online manual Q&A: if students are not satisfied with the AI ​​Q&A results, they can initiate a manual Q&A request. The engine pushes the question to the corresponding teacher's end, synchronously displaying the student's relevant learning data (mastery of the questioned knowledge point, related experiment / practice status), facilitating accurate Q&A by the teacher, and the Q&A record is automatically archived to the student's learning file; Step S6, Synchronization of Learning Data and Dynamic Path Optimization: The intelligent learning engine will synchronize core learning data, including but not limited to student learning ability assessment results, personalized path execution status, and knowledge point mastery, to the home-school collaborative monitoring module in real time, providing data support for the visualization of learning progress and tripartite collaborative intervention. At the same time, it will regularly (every day at midnight) summarize student learning data, update the parameters of the learning ability assessment model, optimize the weight of learning priority calculation, and dynamically adjust personalized learning paths based on student path execution status, Q&A feedback, and test results. For example, if a student's mastery of a weak knowledge point improves to over 80% after intensive learning, the path will be adjusted in a timely manner, and extended resources will be pushed. If a knowledge point still fails to meet the standard after multiple reinforcements, the frequency of basic resource pushes will be increased, and teacher intervention reminders will be pushed simultaneously, forming a closed loop of "data collection-assessment-push-optimization".

[0023] Furthermore, the specific content and sources of the multi-source learning behavior data collected in step S2 include: first, course learning data pushed by the dynamic course management module (course click trajectory, dwell time on key content, course completion rate, test answer results and time consumption); second, experimental operation data pushed by the mathematics experiment integration module (operation steps, parameter adjustment records, experiment completion rate, number of erroneous operations, experiment time consumption); and third, student-side active operation data (Q&A content, supplementary resource viewing records, personalized path execution status). After collection, the data undergoes preliminary cleaning to remove invalid data (such as accidental clicks or abnormal records caused by network interruptions), and is classified and archived according to student ID-knowledge point-collection timestamp to form a structured data set.

[0024] Furthermore, the logical response of "system matching - large model retrieval - manual backup" in step S5 is as follows: First, the system performs resource matching, searching for relevant courses, experiments, and exercises in the dynamic course management module and the integrated mathematics experiment module, and pushing the most relevant resources to the student's question. Second, it searches for answers online; if no matching resources are found in the system, it calls DeepSeek or Doubao AI's large-scale model to retrieve accurate answers and problem-solving strategies, and synchronously associates them with corresponding knowledge points. Next, it recommends related knowledge points, pushing explanations of relevant knowledge points based on the question content to help students apply their knowledge to other situations. Finally, it provides online human Q&A; if students are not satisfied with the AI ​​Q&A results, they can request human Q&A, and the engine will push the question to the corresponding teacher's end, synchronously displaying the student's relevant learning data (mastery of the questioned knowledge points, relevant experiment / exercise status), facilitating accurate Q&A by teachers, and the Q&A record is automatically archived in the student's learning file.

[0025] Furthermore, an online learning method for mathematics tutors, applied to an online mathematics tutoring system, includes the following steps: Step 1, Course Construction and Release: Teachers upload interactive course packages through the dynamic course management module, annotate metadata (knowledge points, grade, difficulty), embed mathematical experiment components and test questions, generate structured courses, and release them to the system; Step 2, Interactive Learning Process: Students log in to the system, select the corresponding course, and simultaneously learn and conduct experiments in split-screen mode. After completing the learning of each knowledge point, they immediately complete the targeted exercises pushed by the system, realizing learning and practice at the same time. Step 3, Data Collection and Personalized Recommendation: The intelligent learning engine collects students' learning behavior data in real time, calculates the mastery of knowledge points through the evaluation model, calls the large model to generate learning reports and personalized learning paths, and pushes supplementary resources or reinforcement exercises for weak knowledge points. Step 4: Home-School Collaborative Intervention: The home-school collaborative monitoring module synchronizes learning data, teachers adjust teaching strategies according to the class's learning situation, parents track students' learning progress, and the three parties work together to complete learning intervention, forming a closed loop in teaching.

[0026] This invention discloses an online mathematics learning system and method, belonging to the field of online education technology. Addressing the technical bottlenecks of existing mathematics learning platforms, such as high development barriers, insufficient interactivity, low personalization, and weak home-school collaboration, this system constructs a four-layer architecture: dynamic course management, embedded mathematical experiments, an intelligent learning engine, and home-school collaborative monitoring. It supports low-barrier uploading and real-time rendering of interactive HTML / JS / CSS course packages, integrates mathematical experiment tools such as GeoGebra / Network Drawing Board, combines AI algorithms to analyze learning behavior data and dynamically plan personalized paths, and simultaneously builds a data-visualized learning monitoring system. This invention realizes a "learning by doing" and "learning by doing" teaching model, reduces teachers' course development costs, enhances students' understanding of abstract mathematical concepts, strengthens the teaching loop through a home-school collaboration mechanism, and provides an intelligent, interactive, and personalized solution for online mathematics education.

[0027] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A mathematical learning companion online learning system, characterized in that, It includes a dynamic course management module, a math experiment integration module, an intelligent learning engine, and a home-school collaborative monitoring module. The dynamic course management module is used to enable the low-threshold construction, uploading, management, and publishing of interactive math courses. It supports teachers to upload interactive course packages containing HTML, CSS, and JS files, embedding various teaching resources and test questions, supporting course metadata annotation, associating with a large model to realize the analysis of weak knowledge points and push learning suggestions, and providing a split-screen synchronous display function to realize the synchronous conduct of course learning and experiments / exercises, providing basic content guarantee for interactive learning. The integrated mathematical experiment module provides students with an embedded mathematical experiment environment. It has a built-in lightweight GeoGebra / network drawing board engine, supports the direct embedding of experimental components on course pages, provides a mathematical experiment template library covering the K-12 stage, and also supports teachers to upload custom experimental files. Students can operate and adjust mathematical model parameters in real time, observe changes in mathematical laws, and the experimental operation is linked to course knowledge points in real time, strengthening the closed loop of experimental operation-theoretical understanding-practice consolidation, and helping students understand abstract mathematical concepts. The intelligent learning engine is used to realize personalized learning push and real-time Q&A, collect students' learning behavior data in real time, build a learning ability assessment model based on knowledge graph and machine learning algorithm, calculate the learning priority of knowledge points, dynamically plan personalized learning paths, and at the same time build a real-time Q&A engine to support system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The intelligent learning engine is used to realize personalized learning push and real-time Q&A, collect students' learning behavior data in real time, build a learning ability assessment model based on knowledge graph and machine learning algorithm, calculate the learning priority of knowledge points, dynamically plan personalized learning paths, and at the same time build a real-time Q&A engine to support system resource matching, online search for Q&A, knowledge point association recommendation and human online Q&A, adapting to the learning pace and ability level of different students. The home-school collaborative monitoring module is used to realize teaching collaboration and closed-loop management among teachers, students and parents. It provides a visual display of learning data, which intuitively presents data including but not limited to students' learning time, answer accuracy, and mastery of knowledge points. It supports teachers to push learning suggestions, supplementary resources and targeted exercises with one click, and allows parents to view students' learning progress and weaknesses in real time. It opens up communication channels among the three parties and realizes data-driven precise teaching intervention.

2. The online learning system for mathematics tutors according to claim 1, characterized in that: The specific implementation logic of the mathematical experiment integration module is as follows: Step 1: Initialize and deploy the experimental engine to build the embedded basic environment: The mathematical experiment integrated module pre-integrates the lightweight GeoGebra engine and the network drawing board engine, completes the compatibility adaptation between the engine and the system front end, ensures that students do not need to download and install additional plugins, and directly embeds the interactive course page published by the dynamic course management module. At the same time, it configures the experimental operation response mechanism to ensure that the response time for adjusting experimental parameters and refreshing images is ≤100ms, adapts to the display and operation requirements of multiple terminals such as Windows, iOS and Android, and achieves seamless integration with the course split-screen mode; Step 2: Experiment Template Library Construction and Custom Experiment Upload Adaptation: First, the system presets an experiment template library covering all math knowledge points in the K-12 stage, and archives them according to the categories of elementary geometry, junior high functions, and senior high statistics and analytic geometry; Secondly, a custom experiment upload interface was developed to support teachers in uploading custom experiment files in .ggb format. After uploading, the system automatically parses the experiment parameters and knowledge point association information, and completes the matching with the course metadata to ensure that the experiment content accurately corresponds to the course knowledge points. Step 3: Embedding and Binding Experiment Components with Course Content: When teachers publish interactive courses through the dynamic course management module, they can select the corresponding experiment template from the experiment template library or upload a custom experiment file on the course editing page. The experiment components are then embedded into the corresponding knowledge point chapters of the course. At the same time, the linkage rules between experiments and courses are set—combined with the course split-screen display function, the experiment components are deployed on the right side of the course page and synchronized with the course content on the left side. This ensures that students can immediately carry out experimental operations when they learn the corresponding knowledge points, realizing learning by doing. This step is also linked to the course metadata annotation function of the dynamic course management module, so that the experiment components and course knowledge points form a one-to-one correspondence, laying the foundation for the subsequent correlation and collection of experiment data and knowledge point mastery. Step 4: Student-side interactive operation, real-time presentation of mathematical patterns: When students log in to the system to learn the corresponding course, they enter the split-screen learning interface, view the course explanation on the left, and click to start the experiment component on the right to carry out real-time operation: adjust the parameters of the mathematical experiment model by dragging, inputting parameters, clicking to trigger, etc. Step 5: Experimental Data Collection and Knowledge Point Reinforcement: After students complete the experimental operation, the experimental integration module automatically collects the experimental operation data and pushes it to the intelligent learning engine in real time for subsequent knowledge point mastery assessment and personalized learning path planning. At the same time, the system automatically triggers the linkage mechanism to push reinforcement exercises for the corresponding knowledge points based on the students' experimental completion. The exercises focus on the mathematical laws verified by the experiment, strengthening the closed loop of experimental operation-theoretical understanding-practice reinforcement. Step 6: Experiment Operation Feedback and Optimization: During the experiment, the mathematics experiment integration module monitors the experimental operation status. If students make mistakes such as incorrect parameter input or unreasonable operation steps, the experimental component will automatically pop up a concise prompt to guide students to correct their operation. At the same time, the experimental integration module regularly summarizes student experimental operation data and teacher feedback to optimize the ease of operation of the experimental template and update the compatibility of the experimental component.

3. The online learning system for mathematics tutors according to claim 1, characterized in that: The specific implementation steps of the intelligent learning engine are as follows: Step S1: Engine Initialization and Basic Configuration, Building the Intelligent Support Environment: The intelligent learning engine core program is pre-deployed, and interface adaptation with the dynamic course management module, mathematics experiment integration module, and home-school collaborative monitoring module is completed. Data collection frequency, algorithm parameter thresholds, and large model call interfaces are configured. At the same time, the K12 stage mathematics knowledge graph is imported, and an association network is built according to the grade level and knowledge point level. The difficulty coefficient of each knowledge point, related knowledge points, and corresponding courses and experimental resources are marked. The learning ability assessment model parameters are initialized to ensure that the engine can receive and process various types of data normally, with a response time of ≤2 seconds, and adapt to multi-terminal usage scenarios. Step S2: Real-time collection and integration of multi-dimensional learning behavior data: The intelligent learning engine collects learning behavior data from multiple sources in real time through preset interfaces to form a complete profile of student learning behavior. Step S3: Calculate the learning ability assessment model to determine the mastery of knowledge points and learning priority. Based on the collected structured data, a pre-set learning ability assessment model is invoked, according to the formula. Perform the calculation, where For the first Learning priorities for each knowledge point For the first The weights for behavioral data are as follows: 0.4 for correct answer rate, 0.3 for experimental operation completion rate, and 0.3 for dwell time. For the first The knowledge point corresponds to the first Standardized score of class behavior, range of values Simultaneously, by combining knowledge graphs, we analyze students' weaknesses in mastering various knowledge points, mark weak knowledge points and related knowledge points, generate preliminary learning ability assessment results, and provide data support for personalized learning path planning. Step S4, Dynamic Planning and Resource Push for Personalized Learning Paths: Based on the learning ability assessment results and the student's grade level and learning progress, a personalized learning path is dynamically planned: for knowledge points with a mastery level of ≥80%, extended resources are pushed. For knowledge points with a mastery level of 60%-80%, reinforcement resources are pushed; for knowledge points with a mastery level of <60%, basic explanation resources are pushed first, followed by targeted exercises, to ensure that the path is adapted to the student's ability level; all pushed resources come from the course library of the dynamic course management module and the experiment library of the mathematics experiment integration module, and at the same time, the large model is called to generate personalized learning suggestions for each learning path and push them to the student's end in real time. Step S5, Real-time Q&A Engine Activation and Multi-mode Q&A Response: When students raise questions during the learning process, the real-time Q&A engine is activated, and the response follows the logic of "system matching - large model retrieval - manual backup". Step S6, Synchronization of Learning Data and Dynamic Path Optimization: The intelligent learning engine will synchronize core learning data, including but not limited to student learning ability assessment results, personalized path execution status, and knowledge point mastery, to the home-school collaborative monitoring module in real time, providing data support for the visualization of learning data and tripartite collaborative intervention; at the same time, it will regularly summarize student learning data, update the parameters of the learning ability assessment model, optimize the weight of learning priority calculation, and dynamically adjust personalized learning paths based on student path execution status, Q&A feedback, and test results. If a certain knowledge point still fails to meet the standard after repeated reinforcement, the frequency of basic resource push will be increased, and teacher intervention reminders will be pushed at the same time to form a closed loop of "data collection-evaluation-push-optimization".

4. The online learning system for mathematics tutors according to claim 3, characterized in that: The specific content and sources of the multi-source learning behavior data collected in step S2 include: first, course learning data pushed by the dynamic course management module; second, experimental operation data pushed by the mathematics experiment integration module; and third, active operation data from the student end. After collection, the data is initially cleaned, invalid data is removed, and the data is classified and archived according to student ID-knowledge point-collection timestamp to form a structured data set.

5. The online learning system for mathematics tutors according to claim 3, characterized in that: The logical response of "system matching - large model retrieval - manual backup" in step S5 is as follows: First, the system performs resource matching, searching for relevant courses, experiments, and exercises in the dynamic course management module and the integrated mathematics experiment module, and pushing the most relevant resources to the question. Second, it searches for answers online. If no matching resources are found in the system, it calls DeepSeek or Doubao AI's large model to retrieve accurate answers and problem-solving strategies, and synchronously associates them with corresponding knowledge points. Finally, it recommends related knowledge points, pushing relevant explanations of knowledge points based on the question content to help students apply what they have learned to other situations. Finally, there is online Q&A with human assistants. If students are not satisfied with the AI's answer, they can request a human assistant. The engine will push the question to the corresponding teacher and display the student's relevant learning data in a synchronized manner, so that the teacher can provide accurate answers. The Q&A record is automatically archived in the student's learning file.

6. A method for online math learning with a peer tutor, applied to the online math learning system described in any one of claims 1-5, characterized in that: Includes the following steps: Step 1, Course Construction and Release: Teachers upload interactive course packages through the dynamic course management module, annotate metadata, embed mathematical experiment components and test questions, generate structured courses, and release them to the system; Step 2, Interactive Learning Process: Students log in to the system, select the corresponding course, and simultaneously learn and conduct experiments in split-screen mode. After completing the learning of each knowledge point, they immediately complete the targeted exercises pushed by the system, realizing learning and practice at the same time. Step 3, Data Collection and Personalized Recommendation: The intelligent learning engine collects students' learning behavior data in real time, calculates the mastery of knowledge points through the evaluation model, calls the large model to generate learning reports and personalized learning paths, and pushes supplementary resources or reinforcement exercises for weak knowledge points. Step 4: Home-School Collaborative Intervention: The home-school collaborative monitoring module synchronizes learning data, teachers adjust teaching strategies according to the class's learning situation, parents track students' learning progress, and the three parties work together to complete learning intervention, forming a closed loop in teaching.

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