A learning sequence generation method based on learning relations

Abstract

The present invention relates to a learning sequence generation method based on learning relationships, and belongs to the field of graph data analysis and mining. The method comprises: obtaining the learning status and dependency relationship of knowledge points in the first knowledge graph from the first knowledge graph, wherein the learning status includes mastered, learned but not mastered, and unlearned but not mastered; taking any mastered knowledge point in the first knowledge graph as the starting point, merging the mastered knowledge points with which there is a direct dependency relationship, generating a second knowledge graph, wherein the mastered knowledge points after merging retain the dependency relationship with the unmastered knowledge points; from the second knowledge graph, selecting the unlearned and unmastered knowledge points with which there is a direct dependency relationship with the mastered knowledge points as the starting point, generating multiple learning sequences. The method can dynamically generate multiple sequences according to the characteristics of the mathematics subject, combined with the learning status of the knowledge points and the dependency relationship between the knowledge points, and formulate a personalized and efficient learning plan.

Description

Technical Field

[0001] The present invention relates to the field of graph data analysis and mining, and in particular to a learning sequence generation method based on learning relationships. Background Art

[0002] Knowledge acquisition is an incremental process, and the learning of new knowledge depends on the knowledge already mastered by the learner. This learning dependency manifests itself in the prerequisite knowledge required to learn a particular knowledge point. According to modern cognitive science theory, navigational learning based on learning dependencies is an effective means of reducing cognitive load. The key issue is how to automatically generate the shortest learning sequence based on the learning dependencies between knowledge points and the learner's target knowledge points.

[0003] Mathematical knowledge is characterized by abstraction, precision, and logic. Mathematical learning is also the focus and difficulty of learning activities. The logic of mathematical knowledge is manifested in the strong correlation between the learning order of mathematical knowledge points. The learning path planning method in related technologies constructs a knowledge map for student learning and plans a learning path with knowledge points as the basic unit based on the learning dependency relationship of knowledge points, in order to achieve the shortest generated learning sequence. However, the planning of this type of method is static, the planned path is unreasonable, and it does not take into account the characteristics of the mathematical discipline, making it difficult to implement. Summary of the Invention

[0004] In order to solve the problems existing in the prior art, the present invention discloses a learning sequence generation method based on learning dependency, which can dynamically plan and adjust the learning sequence of mathematical knowledge according to the knowledge points that learners want to learn while satisfying the learning dependency, thereby improving learning efficiency.

[0005] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is a learning sequence generation method based on learning relationships, comprising the following steps: a first step: obtaining the learning status of the knowledge points in the knowledge graph and the dependency relationship between the knowledge points from the first knowledge graph, wherein the learning status includes mastered, learned but not mastered, and not learned but not mastered. If the knowledge point after learning needs to rely on the previous knowledge point that has been mastered, there is a dependency relationship between the knowledge points; a second step: taking any mastered knowledge point in the first knowledge graph as the starting point, merging the mastered knowledge points that have a direct dependency relationship with it, the mastered knowledge points after merging retain the dependency relationship with the unmastered knowledge points, deleting isolated knowledge points, and generating a second knowledge graph; a third step: generating a second knowledge graph from the second knowledge graph In the spectrum, select the unlearned and unmastered knowledge points that have a direct dependency relationship with the mastered knowledge points as the starting point to generate one or more first learning sequences; the fourth step: if there are multiple first learning sequences, select a first learning sequence with the longest learning path as the second learning sequence, otherwise, select the only first learning sequence as the second learning sequence; the fifth step: starting from the last knowledge point in the second learning sequence, gradually update the knowledge points in the second learning sequence in reverse order to generate a target learning sequence; wherein, updating the knowledge points in the second learning sequence includes: if there are multiple previous knowledge points in the second knowledge graph for the latter knowledge point in the second sequence, then merge the multiple previous knowledge points into the previous knowledge points of the latter knowledge point in the second sequence.

[0006] In some embodiments, the learning status of a knowledge point is obtained by automatically recording and analyzing the learner's learning behavior data or the learner's input through the learning system. Thus, the present invention can efficiently and timely update the knowledge graph and learning sequence.

[0007] In some embodiments, the learning status is determined based on the learner's test scores on relevant knowledge points. The test scores can more accurately detect the learner's learning status on the knowledge points.

[0008] In some embodiments, when generating the second knowledge graph, the merged knowledge points are marked to distinguish them from the unmerged knowledge points. The merge mark can be removed, and the merged knowledge points after the mark is removed can be restored. Based on this, the second knowledge graph in this application can be restored, thereby preventing misoperation or adjustments based on human settings.

[0009] In some embodiments, the fourth step "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically as follows: if there are multiple first learning sequences with the longest learning paths, then selecting the first learning sequence with the most directly dependent knowledge points in the second knowledge graph as the second learning sequence. In this way, a learning sequence of knowledge points with more extensive connections can be constructed, which is conducive to more systematic learning for learners.

[0010] In some embodiments, the fourth step of "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically: if there are multiple first learning sequences with the longest learning paths, then select the first learning sequence with the least directly dependent knowledge points in the second knowledge graph as the second learning sequence.

[0011] In this way, a more lightweight learning sequence of knowledge points can be constructed, which helps learners master knowledge more quickly.

[0012] In some embodiments, the learning status and dependencies in the first knowledge graph are regularly updated to ensure the timeliness and accuracy of the learning sequence. This allows the learning system to more timely and accurately grasp the learner's learning status and learning plan progress, and develop more personalized learning strategies.

[0013] In some embodiments, a visual display of the learning sequence is provided, which can improve the usability and friendliness of the system.

[0014] In some embodiments, learners are allowed to provide feedback and evaluation on the generated learning sequence, and the system adjusts the generation strategy of the learning sequence based on the feedback. By accepting user feedback, the learning sequence and the learner's learning plan can be adjusted in a timely manner to improve learning efficiency.

[0015] In some embodiments, the learning sequence is associated with the learning resource. By associating the learning sequence with the learning resource, the learner can obtain the learning resource in a timely manner by clicking on the knowledge point on the client, which increases the convenience of using the system and thus improves learning efficiency.

[0016] In some embodiments, the method further includes recording the learner's learning progress and performance during the learning sequence, and regenerating the target learning sequence if there are any knowledge points that have been learned but not mastered. This allows for timely adjustments to the learning plan based on the learner's characteristics, thereby improving learning efficiency.

[0017] Compared to existing technologies, this invention generates an optimized learning sequence based on the learning status and dependencies of knowledge points in the middle school mathematics knowledge graph, incorporating the characteristics of mathematical knowledge. By analyzing and processing the knowledge graph, starting from the knowledge points already mastered, it gradually derives a target learning sequence suitable for further learning, thereby improving learning efficiency and effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the learning sequence generation process based on learning relationships in some embodiments of the present application.

[0019] Figure 2 This is a schematic diagram of the first knowledge graph in some embodiments of the present application.

[0020] Figure 3 This is a schematic diagram of the second knowledge graph in some embodiments of the present application.

[0021] Figure 4 Schematic diagram of multiple first learning sequences in some embodiments of the present application.

[0022] Figure 5 Schematic diagram of the second learning sequence in some embodiments of the present application.

[0023] Figure 6 This is a schematic diagram of an online learning platform in some embodiments of the present application.

[0024] Figure 7 This is a schematic diagram of a learning system in some embodiments of the present application.

[0025] Figure 8 This is a target learning sequence in some embodiments of the present application. DETAILED DESCRIPTION

[0026] During the learning process of middle school mathematics, students need to face numerous knowledge points, and there are complex dependencies between these knowledge points. Traditional learning methods often fail to effectively utilize these dependencies, resulting in problems such as unreasonable learning order and low learning efficiency during the learning process. The learning relationship-based learning sequence generation method proposed in this patent aims to provide a scientific and efficient learning sequence planning solution for middle school mathematics learning, helping students better master knowledge.

[0027] The present invention relates to the field of educational technology, and in particular to a learning relationship-based learning sequence generation method applied to middle school mathematics learning.

[0028] The vast body of secondary school mathematics encompasses a wide range of areas, including algebra, geometry, functions, and statistics. For example, in algebra, learning linear equations forms the foundation for subsequent learning of systems of linear equations in two variables and quadratic equations. In geometry, the properties and theorems of triangles form the foundation for further study of geometric shapes such as quadrilaterals and polygons. However, students often simply follow the textbook's sequence or the teacher's instructions, without fully considering the inherent dependencies between key knowledge points. This can lead students to progress without fully mastering the underlying knowledge points, increasing learning difficulty and reducing learning efficiency.

[0029] Most existing learning assistance tools or methods simply list and explain knowledge points, without considering the learning status and dependencies of knowledge points to plan learning sequences. Therefore, it is necessary to develop a new method to generate learning sequences that are suitable for individual students.

[0030] The core of this invention is to generate an optimized learning sequence based on the learning status and dependencies of knowledge points in the middle school mathematics knowledge graph, combined with the characteristics of mathematical knowledge. By analyzing and processing the knowledge graph, starting from the knowledge points already mastered, a target learning sequence suitable for further learning is gradually derived, thereby improving learning efficiency and effectiveness.

[0031] Figure 1 Schematic diagram of the learning sequence generation process based on learning relationship in some embodiments of the present application. Figure 1 As shown, the method in this case includes 5 basic steps.

[0032] Step 1: Obtain the learning status of the knowledge points in the first knowledge graph and the dependency relationship between the knowledge points, wherein the learning status includes mastered, learned but not mastered, and not learned but not mastered.

[0033] Figure 2 is a schematic diagram of the first knowledge graph in some embodiments of the present application. Figure 2 As shown, the first knowledge graph is the initial graph at a certain moment. The first knowledge graph can be a newly established graph or the knowledge graph of a certain knowledge graph at a certain moment. The first knowledge graph is generally composed of multiple knowledge points. It is understood that in some situations, the first knowledge graph can be composed of a single knowledge point. In addition, the first knowledge graph also includes the learning relationships (i.e., dependencies) between knowledge points.

[0034] In the middle school mathematics knowledge map, each knowledge point has its own unique learning status. For example, for the knowledge point of linear equations, if a student can skillfully solve various types of linear equations and understand their concepts and applications, then the learning status of this knowledge point is mastered (including knowledge points that have been mastered without learning them); if a student can solve some simple linear equations but has difficulty with complex problems or understanding the concepts, then the knowledge point is learned but not mastered; if a student has not yet been exposed to this knowledge point, then the knowledge point is not learned or mastered. The learning status can be represented by a flag bit in the knowledge point. For example, a learning status of s=11 or 10 indicates mastered, a learning status of s=01 indicates learned but not mastered, and s=00 indicates not learned or mastered.

[0035] At the same time, there are rich dependencies between knowledge points. If the knowledge points learned later need to rely on the previous knowledge points that have been mastered, then there are dependencies between the knowledge points. Taking function knowledge as an example, the learning of linear functions depends on the knowledge of linear equations, because the expression of linear functions is closely related to linear equations. When solving problems such as the intersection of linear functions and coordinate axes, the solution of linear equations is needed. We can construct a middle school mathematics knowledge map through various means such as analyzing textbook content, teaching outlines, and the experience of educational experts, and obtain these learning status and dependency information from them. Dependency relationships can be represented by "→", for example, A→B means that the learning of knowledge point B is based on the mastery of knowledge point A. In this case, B is the subsequent knowledge point and A is the previous knowledge point.

[0036] It can be understood that the learning state represents the characteristics of each knowledge point itself, while the dependency relationship is the relationship between a knowledge point and other knowledge points.

[0037] The purpose of this step is to obtain the current learner's mastery of the knowledge points and the learning relationship between the knowledge points, so as to facilitate the operation of the subsequent steps.

[0038] The second step: starting from any mastered knowledge point in the first knowledge graph, merge the mastered knowledge points that have a direct dependency relationship with it, retain the dependency relationship between the merged mastered knowledge points and the unmastered knowledge points, delete the isolated knowledge points, and generate the second knowledge graph.

[0039] The purpose of this step is to simplify the knowledge graph. By merging the acquired knowledge points and deleting isolated knowledge points, the knowledge graph can be simplified, making it clearer and easier to process later.

[0040] In this case, a "direct dependency" refers to a direct learning relationship. For example, in the first knowledge graph, knowledge points A and C, and C and D, have direct dependencies, while A and D have an indirect dependency. An "isolated knowledge point" is one that has no dependencies on other knowledge points. This means that learning this knowledge point does not rely on learning or mastering other knowledge points, and the learning or mastery of other knowledge points does not presuppose the mastery or learning of this knowledge point.

[0041] In this case, for knowledge points that have a direct dependency relationship, such as knowledge point F and knowledge point I, the learning of knowledge point I depends on the learning of knowledge point F. Therefore, knowledge point F is called the predecessor knowledge point of knowledge point I, and knowledge point I is called the successor knowledge point of knowledge point F. It should be noted that the predecessor knowledge and successor knowledge points are not necessarily unique. For example, knowledge point I has multiple predecessor knowledge points, and knowledge point B has multiple successor knowledge points.

[0042] Figure 3 is a schematic diagram of the second knowledge graph in some embodiments of the present application. Figure 2-3 As shown, assuming that in the first knowledge graph, knowledge points A, C, and D are already mastered knowledge points, and J is an isolated knowledge point, the knowledge graph after the second step is as follows Figure 3 shown.

[0043] Suppose that in the knowledge graph for middle school algebra, the mastered knowledge point is a linear equation. This has a direct dependency on a system of linear equations with two variables (because both the substitution and addition / subtraction methods for solving a system of linear equations with two variables are related to the solution of linear equations with one variable). At the same time, linear equations with one variable also have a dependency on linear inequalities with one variable (the steps for solving linear inequalities with one variable are similar to those for linear equations with one variable). Starting with the linear equation with one variable, we merge the mastered knowledge points of the system of linear equations with two variables and linear inequalities with one variable, retaining their dependencies with unmastered knowledge points (such as the system of linear equations with three variables, whose solution is somewhat related to the system of linear equations with two variables and is currently assumed to be unmastered by the student), and removing isolated knowledge points (such as an ancient mathematical algorithm knowledge point that is unrelated to the currently mastered and related unmastered knowledge points), thereby generating a second knowledge graph.

[0044] By merging the mastered knowledge points that have direct dependencies one by one, all the mastered knowledge points in a certain area of ​​the knowledge graph will become one mastered knowledge point. At the same time, the merged mastered knowledge point retains the dependency relationship with the unmastered knowledge points, which is convenient for subsequent processing.

[0045] Step 3: From the second knowledge graph, select unlearned and unmastered knowledge points that have a direct dependency on the mastered knowledge points as starting points to generate one or more first learning sequences.

[0046] After the previous step, the second knowledge graph obtained has been greatly simplified. Through this step, multiple first learning sequences will be obtained. This step selects unlearned and unmastered knowledge points that have a direct dependency on already mastered knowledge points as the starting point of the learning sequence. Knowledge points that have been learned but not mastered should not be used as the starting point of the learning sequence. This can improve learning efficiency and avoid wasting too much time on a difficult knowledge point. At the same time, unlearned and unmastered knowledge points that do not have a direct dependency on already mastered knowledge points should not be used as the starting point of the learning sequence. Such knowledge points should be used as intermediate nodes or terminal nodes of the learning sequence.

[0047] It's important to note that if the learning of an unlearned or unmastered knowledge point doesn't rely on a mastered knowledge point, then that node is considered an unlearned or unmastered knowledge point with a direct dependency on the mastered knowledge point. It's understandable that this type of knowledge point actually has a mastered knowledge point with a direct dependency, but it's not shown on the knowledge graph. Taking the second knowledge graph as an example, if knowledge point B is an unlearned or unmastered knowledge point, then that knowledge point can serve as the starting point for the learning sequence.

[0048] Figure 4 Schematic diagram of multiple first learning sequences in some embodiments of the present application. Figure 4 As shown, with knowledge point B as the starting point, 4 first learning sequences can be obtained, some of which have 4 knowledge points, and some have 5 knowledge points.

[0049] From the second knowledge graph, we start with unlearned or unmastered knowledge points that have a direct dependency on already mastered knowledge points. For example, starting with a system of linear equations, we can generate a learning sequence based on the dependency relationship: system of linear equations → system of linear equations with two variables → system of linear equations with three variables. Furthermore, if there are other unlearned or unmastered knowledge points, such as quadratic functions (which have a dependency relationship with linear equations in terms of the function-equation relationship), we can generate another learning sequence: system of linear equations → quadratic functions. This generates multiple first learning sequences.

[0050] Step 4: If there are multiple first learning sequences, then select a first learning sequence with the longest learning path as the second learning sequence; otherwise, select a unique first learning sequence as the second learning sequence.

[0051] Compare the lengths of the learning paths among the generated multiple first learning sequences. Assuming the two learning sequences mentioned above, the first learning sequence has three knowledge points, and the second learning sequence has two knowledge points. Then, choose the first learning sequence (system of linear equations with one variable → system of linear equations with two variables → system of linear equations with three variables) as the second learning sequence because it has the longest learning path and covers the review and consolidation of more relevant knowledge points.

[0052] In related art, a learning sequence with a shorter learning path tends to be chosen, while in this case, a longer learning sequence was chosen. Mathematical knowledge is characterized by high learning difficulty, strong logic, and strong knowledge coherence and relevance. Considering the characteristics of mathematics, choosing a learning sequence with a longer path can provide learners with timely motivational feedback and enhance their interest in learning. Furthermore, a learning sequence with a longer learning path can integrate as many knowledge points as possible, establishing a learning logic with basic knowledge points as the main thread, connecting the entire middle school mathematics knowledge points and establishing a framework for learners' mathematical thinking.

[0053] In some embodiments, the fourth step "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically as follows: if there are multiple first learning sequences with the longest learning paths, then selecting the first learning sequence with the most directly dependent knowledge points in the second knowledge graph as the second learning sequence. In this way, a learning sequence of knowledge points with more extensive connections can be constructed, which is conducive to more systematic learning for learners.

[0054] In some embodiments, the fourth step of "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically: if there are multiple first learning sequences with the longest learning paths, then select the first learning sequence with the least directly dependent knowledge points in the second knowledge graph as the second learning sequence.

[0055] In this way, a more lightweight learning sequence of knowledge points can be constructed, which helps learners master knowledge more quickly. Figure 5 Schematic diagram of the second learning sequence in some embodiments of the present application. Figure 5 As shown, two first learning sequences with five knowledge points are selected as the second learning sequence. Any one of the two learning sequences can be used as the second learning sequence.

[0056] Step 5: Taking the last knowledge point in the second learning sequence as the starting point, gradually update the knowledge points in the second learning sequence in reverse order to generate a target learning sequence; wherein, updating the knowledge points in the second learning sequence includes: if there are multiple previous knowledge points in the second knowledge graph for the latter knowledge point in the second sequence, then merging the multiple previous knowledge points into the previous knowledge points of the latter knowledge point in the second sequence.

[0057] Figure 8This is the target learning sequence in some embodiments of the present application. Taking the second learning sequence B→ACD→E→F→I as an example, in the second knowledge graph, for knowledge point I, the learning of knowledge point I depends on GFH. Therefore, during the update process, knowledge points G, F, and H are merged into one knowledge point GFH. After the update, the target learning sequence B→ACD→E→GFH→I is obtained. This learning sequence has more knowledge points and is more conducive to systematic knowledge mastery.

[0058] Starting with the last knowledge point in the second learning sequence (a linear equation), the learning sequence is updated in reverse order. In the second knowledge graph, if there are knowledge points in the second learning sequence that are directly dependent on the linear equation and also have knowledge points related to inequalities (such as a linear inequality), then the linear inequality is merged as the previous knowledge point of the linear equation. The updated learning sequence becomes: linear inequality + linear equation → system of linear equations → system of linear equations. Continue the reverse update. If knowledge related to the linear inequality is found to be related to the system of linear equations (assuming it was not previously considered), further merge them, ultimately generating the target learning sequence. This target learning sequence helps students systematically learn related knowledge they have not yet mastered, starting from the knowledge they have already mastered, and fully considers the dependencies between knowledge points.

[0059] This example was conducted on an online middle school mathematics learning platform. This platform maintains a comprehensive database of middle school mathematics knowledge, including detailed explanations of each knowledge point, examples, and exercises. Furthermore, the platform records each student's progress in learning each knowledge point, comprehensively assessing their learning status based on various data, including practice results, test scores, and study time.

[0060] Figure 6 Schematic diagram of the online learning platform in some embodiments of the present application. Figure 6 As shown in Figure 1, the learning system in this case includes learners, a server, and multiple clients. Learners learn through the learning interface provided by the client, and the client records the learner's learning behavior. The server is responsible for processing the data from the client and providing the processed data to the learner through the client.

[0061] Learners are the primary users of this learning system, accessing it to acquire knowledge and improve their skills. The client presents learners with an intuitive and user-friendly learning interface. This interface is designed to be concise and easy to navigate, allowing learners to quickly find the learning resources they need, such as the course catalog and study materials. For example, the interface might present courses across different disciplines and difficulty levels in a categorized menu, allowing learners to easily access the course pages of their interest. As learners use the learning interface, the client records their learning behavior in detail. This includes, but is not limited to, the duration of each course module, the order in which they study, their responses (if there are practice or test sessions), and the number of times they pause and replay the video. For example, when a learner is watching a math video, the client records the time they pause the video at a certain point and whether they subsequently replay that section. This information provides an indication of the learner's level of difficulty in understanding that point.

[0062] The server receives learner behavior data from each client. It uses advanced data processing algorithms to analyze and process this data. For example, based on learners' test-answer data, the server can determine which knowledge points the learner has a low accuracy rate on and which ones they have mastered well. For study time data, the server can analyze trends in learners' time spent on different types of courses to understand their learning preferences. This processed data is then fed back to the learner via the client. For example, if the server identifies a learner's weakness in a particular sub-item of English grammar, it will push targeted learning suggestions to the learner through the client, such as relevant specialized exercises, supplementary materials, or recommendations for other courses that cover this topic in more depth. It also displays overall performance trends, such as progress toward completion and changes in learning efficiency, to help learners better understand their learning progress.

[0063] Figure 7 Schematic diagram of the learning system in some embodiments of the present application. Figure 7 As shown in FIG, the learning system includes a learning layer, a computing layer, a communication interface layer, and a database.

[0064] The application layer is the most direct interface between the learning system and learners and clients. It is responsible for presenting various learning functions and services to learners, such as course management, learning plan development, and learning achievement presentation. For example, learners can set their own learning goals and plans at the application layer. Based on these settings, the application layer generates personalized learning path recommendations for learners, tracks the execution of plans during the learning process, and reminds learners to complete various learning tasks.

[0065] The computing layer undertakes the primary computational tasks in the system. It leverages its powerful computing capabilities to conduct in-depth mining and analysis of learning data. For example, it uses complex algorithms to calculate similarities between learners in order to recommend courses or learning methods chosen by other learners with similar learning patterns and good results. The computing layer also handles various model operations within the learning system, such as building personalized learning models based on a learner's historical learning data and predicting potential difficulties and learning outcomes in different learning scenarios.

[0066] The communication interface layer ensures stable and efficient communication between the server and each client. It can handle large amounts of concurrent data transmission. Whether learners' client-side operation data is uploaded to the server, or server-processed feedback data is transmitted back to the client, the communication interface layer ensures data integrity and timeliness. For example, during peak learning times with high concurrency, such as evenings or weekends, the communication interface layer can ensure that data interaction between each client and server is not affected through optimized communication protocols and data caching mechanisms, ensuring a smooth learning experience for learners.

[0067] The database is the data storage center for the entire learning system. It stores a vast amount of learning resources, including videos, documents, and audio materials from various courses. It also stores all learners' personal information, learning history, and learning behavior records. For example, when a learner needs to revisit a previously taken course, the database can quickly and accurately retrieve relevant course materials and information about the learner's progress in that course, supporting their continued learning. Furthermore, the database regularly performs data backup and optimization to ensure data security and efficient system operation.

[0068] The Middle School Mathematics Knowledge Map covers all math content from the seventh through ninth grade. For example, the algebra section includes numbers and expressions (rational numbers, irrational numbers, integers, fractions, etc.), equations and inequalities (linear equations, systems of linear equations, quadratic equations, linear inequalities), and functions (linear functions, quadratic functions, inverse proportional functions). Geometry covers triangles (properties of triangles, congruent triangles, similar triangles, etc.), quadrilaterals (parallelograms, rectangles, rhombuses, squares, etc.), and circles. Statistics and probability also cover topics such as data collection and organization and probability calculations.

[0069] In algebra, the rules for calculating rational numbers are the foundation of calculating expressions. Because the coefficients in expressions are all rational numbers, proficiency in adding, subtracting, multiplying, and dividing rational numbers affects how to calculate expressions. For example, in addition, the coefficients (rational numbers) of like terms must be added together.

[0070] Regarding equations, a linear equation is the basis for a system of linear equations in two variables. Solving a system of linear equations in two variables involves expressing one unknown number using an expression containing another unknown number, then substituting it into another equation to eliminate the unknown number. This process involves solving a linear equation in one variable.

[0071] In geometry, the triangle interior angle theorem is the basis for deriving the polygon interior angle formula. A polygon can be split into multiple triangles, and the triangle interior angle theorem can be used to derive the polygon interior angle formula.

[0072] In the function section, the graph of a linear function is a straight line. The concepts of its slope and intercept are closely related to the coefficients of a linear equation. Solving for the coordinates of the intersection of a linear function and the coordinate axis is to set ∂(x) / ...

[0073] In the Statistics and Probability section, the collection and organization of data is the foundation for calculating probability. Only by accurately collecting and organizing data can we accurately calculate the frequency of events and, therefore, estimate their probability.

[0074] For each student, the platform determines the learning status of a knowledge point based on the following:

[0075] Mastered: If a student achieves over 90% accuracy in the exercises related to the knowledge point, and answers all questions related to the knowledge point correctly in the most recent chapter test, and the cumulative time spent studying the knowledge point exceeds a certain threshold (set based on the difficulty of the knowledge point, such as 1 hour for simple knowledge points and 3 hours for complex knowledge points), the student is considered to have mastered the knowledge point.

[0076] Learned but not mastered: The student's accuracy rate in the exercises related to the knowledge point is between 60% and 90%, or there are some errors in the questions related to the knowledge point in the chapter test, and the study time reaches a certain level (such as 0.5 hours for simple knowledge points and 2 hours for complex knowledge points).

[0077] Not learned and not mastered: If the student has never been exposed to the learning materials related to the knowledge point, or the learning time is extremely short (lower than the time threshold set above), it will be judged as not learned and not mastered.

[0078] The first step is an example. For a student learner, the platform retrieves information from their knowledge graph. In algebra, the learner's learning status for linear equations is "mastered," while their learning status for quadratic equations is "learned but not mastered" (they can solve some simple quadratic equations, but often make mistakes when applying Vieta's theorem). Higher-order equations (such as cubic equations) are "neither learned nor mastered." In geometry, the learner has mastered the properties of triangles, but has learned but not mastered the theorem for determining similar triangles (sometimes confusing different methods), and has not learned or mastered knowledge about circles.

[0079] At the same time, the platform clarifies the dependencies between knowledge points. For example, in algebra, the methods for solving quadratic equations (such as the matching method and the formula method) are dependent on operations such as transposing terms and formulas for linear equations. In geometry, determining similar triangles is dependent on the triangle interior angle theorem and the proportional relationship between sides.

[0080] Example of executing the second step. Suppose the learner has already mastered the knowledge points of linear equations and multiplication of integers in the algebra section. Starting with the linear equation, the platform finds that it has a direct dependency on the multiplication of integers (the multiplication of integers may be involved in the denominator removal step of solving the linear equation), and merges them. At the same time, it deletes isolated knowledge points that are irrelevant to the currently mastered and unmastered knowledge points, such as a certain ancient mathematical notation method (which has little relevance in current middle school mathematics learning and subsequent learning), and generates a second knowledge graph. In this second knowledge graph, the dependency relationship with the unmastered knowledge points (such as the factorization method for solving quadratic equations, which has a certain relationship with the multiplication of integers) is retained.

[0081] Example of executing the third step. From the newly generated second knowledge graph, select unlearned and unmastered knowledge points that have a direct dependency on already mastered knowledge points as starting points. For learners, in the algebra section, starting with factoring quadratic equations, generate a first learning sequence: linear equations (consolidation) → multiplication of integers (review) → factoring quadratic equations. If there are other unlearned and unmastered knowledge points, such as fractional equations (the denominator removal step in their solution is related to multiplication of integers), another learning sequence can be generated: fractional equations → multiplication of integers → linear equations. This generates multiple first learning sequences for learners in the algebra section.

[0082] The fourth step is to perform an example. Compare the learning path lengths of these first learning sequences. Assume that the first learning sequence mentioned above has three knowledge points, and the second learning sequence has three knowledge points (this is just an example; actual results may be different). Further compare the depth of connections and coverage between knowledge points. If the first learning sequence is more comprehensive in reviewing and consolidating related knowledge (for example, covering more types of integer multiplication and the application of linear equations to factoring), then select the first learning sequence as the second learning sequence.

[0083] Example of executing the fifth step. Starting with the last knowledge point in the second learning sequence (linear equations), gradually update in reverse order. In the second knowledge graph, it is discovered that there are also knowledge points related to the application of linear equations (such as travel problems and engineering problems) that are directly dependent on linear equations. These knowledge points are merged as the previous knowledge points of linear equations, and the updated learning sequence becomes: Factoring quadratic equations → Multiplication of integers → Application of linear equations → Linear equations. Continue updating in reverse order. If it is discovered that quantitative relationship analysis knowledge points in practical problems are also related to the application of linear equations, continue merging them, ultimately generating a target learning sequence suitable for the learner. This helps them build on their existing knowledge and more efficiently learn the factoring method for solving quadratic equations, a knowledge point they haven't mastered, while also consolidating relevant basic and related knowledge.

[0084] For students about to learn a new chapter, such as the circle chapter in the ninth grade of junior high school, the platform uses the method described in this invention to generate a preview learning sequence based on the student's previous knowledge of geometry (e.g., knowledge of triangles, quadrilaterals, etc.). Starting from the basic geometry knowledge already mastered, the platform identifies the dependencies between knowledge points related to circles and generates a learning sequence. This allows students to specifically understand the connection between circles and previous knowledge during the preview process, thereby better understanding the new content.

[0085] During the final exam review phase, for students with limited overall algebra knowledge, the platform generates a review sequence based on the student's learning status across various algebraic knowledge points (from numbers and expressions to equations and inequalities, functions, etc.). For example, starting with a linear equation already mastered, the platform uses knowledge graphs and dependency relationships to identify a review order for the entire algebra section, determining which knowledge points to review first to better understand and consolidate other knowledge points, thereby improving review efficiency.

[0086] For students who have extra time and want to expand their mathematical knowledge, the platform can generate learning sequences based on the dependencies between the expanded parts of the middle school mathematics knowledge graph (such as competition-related knowledge points) and the regular teaching knowledge points. For example, starting from the function knowledge already mastered, a learning sequence is generated for students to guide them to learn advanced function knowledge, such as function iteration, fixed points, and other competition-related content, helping them gradually deepen their knowledge.

[0087] By comparing the time students spend completing the same learning task (such as mastering a new knowledge point or reviewing a chapter) before and after using this method, if the time spent by students is significantly reduced (for example, by more than 20%) after using this method, it means that learning efficiency has been significantly improved.

[0088] By analyzing students' scores on exercises and tests related to knowledge points, if students' accuracy rates on tests related to knowledge points significantly improve (e.g., by more than 15%) after learning using the learning sequence generated by this method, it indicates that their mastery of the knowledge points has improved.

[0089] By analyzing the degree of match between the student's learning path and the knowledge point dependency relationships in the knowledge graph, if the student's learning path is highly consistent with the dependency relationships (for example, the learning order of more than 80% of the knowledge points conforms to the dependency relationships), the learning path is reasonable.

[0090] After a one-semester experiment with 100 middle school students, it was found that students who used this method had a significant improvement in learning efficiency. In the new knowledge point learning task, the average learning time was reduced by approximately 25%. In terms of knowledge point mastery, test scores increased by an average of approximately 20%. At the same time, analysis of student learning paths showed that approximately 85% of student learning paths matched well with the dependency relationships in the knowledge graph, indicating that the learning sequence generation method of the present invention has a good application effect in middle school mathematics learning.

[0091] The learning sequence generation method based on learning relationships of the present invention patent is of great significance in middle school mathematics learning. By scientifically analyzing the learning status and dependency relationships of knowledge points, a personalized learning sequence is generated for students, which can effectively improve learning efficiency and the mastery of knowledge points. It has good application effects in learning scenarios such as preview, review and knowledge expansion, and provides an innovative auxiliary learning method for middle school mathematics education. In future development, the construction of knowledge graphs and the judgment method of learning status can be further optimized to better meet the learning needs of different students. At the same time, this method can be expanded to other subject areas to provide more powerful support for students' comprehensive learning.

[0092] In some embodiments, the learning status of a knowledge point is obtained by automatically recording and analyzing the learner's learning behavior data or the learner's input through the learning system. Thus, the present invention can efficiently and timely update the knowledge graph and learning sequence.

[0093] In some embodiments, the learning status is determined based on the learner's test scores on relevant knowledge points. The test scores can more accurately detect the learner's learning status on the knowledge points.

[0094] In some embodiments, when generating the second knowledge graph, the merged knowledge points are marked to distinguish them from the unmerged knowledge points. The merge mark can be removed, and the merged knowledge points after the mark is removed can be restored. Based on this, the second knowledge graph in this application can be restored, thereby preventing misoperation or adjustments based on human settings.

[0095] In some embodiments, in the fourth step, "Step 4: Selecting one of the one or more first learning sequences with the longest learning path as the second learning sequence," if there are multiple first learning sequences with the longest learning paths, the first learning sequence with the most knowledge points directly dependent on the first learning sequence is selected as the second learning sequence. This allows for the construction of a learning sequence with more broadly connected knowledge points, facilitating more systematic learning for learners.

[0096] In some embodiments, in the fourth step "Step 4: Selecting one of the one or more first learning sequences with the longest learning path as the second learning sequence," if there are multiple first learning sequences with the longest learning paths, then the first learning sequence with the least direct dependencies on the knowledge points in the first learning sequence is selected as the second learning sequence. This allows for the construction of a more lightweight learning sequence of knowledge points, helping learners master knowledge more quickly.

[0097] In some embodiments, the learning status and dependencies in the first knowledge graph are regularly updated to ensure the timeliness and accuracy of the learning sequence. This allows the learning system to more timely and accurately grasp the learner's learning status and learning plan progress, and develop more personalized learning strategies.

[0098] In some embodiments, a visual display of the learning sequence is provided, which can improve the usability and friendliness of the system.

[0099] In some embodiments, learners are allowed to provide feedback and evaluation on the generated learning sequence, and the system adjusts the generation strategy of the learning sequence based on the feedback. By accepting user feedback, the learning sequence and the learner's learning plan can be adjusted in a timely manner to improve learning efficiency.

[0100] In some embodiments, the learning sequence is associated with the learning resource. By associating the learning sequence with the learning resource, the learner can obtain the learning resource in a timely manner by clicking on the knowledge point on the client, which increases the convenience of using the system and thus improves learning efficiency.

[0101] In some embodiments, the method further includes recording the learner's learning progress and performance during the learning sequence, and regenerating the target learning sequence if there are any knowledge points that have been learned but not mastered. This allows for timely adjustments to the learning plan based on the learner's characteristics, thereby improving learning efficiency.

[0102] The knowledge graph update mechanism in this case. As students progress through their studies, the learning status and dependencies within the knowledge graph may change. For example, updates to textbook content may lead to adjustments in the dependencies between knowledge points, or a student's learning status may change after relearning a certain knowledge point. Therefore, regularly updating the primary knowledge graph (e.g., weekly or monthly) is key to ensuring the timeliness and accuracy of the learning sequence.

[0103] When updating learning status, the system reanalyzes the student's recent learning data, including new practice results, test scores, and changes in study time. For updates to dependencies, the platform considers the advice of education experts, new syllabi, and the latest textbook content. For example, if a new textbook adjusts the order in which functions are taught or adds content connecting functions with other knowledge points, the system will modify the dependencies in the knowledge graph accordingly, ensuring that the subsequent learning sequence meets the latest teaching requirements.

[0104] The platform provides students with a visual display interface for learning sequences. Learning sequences are presented graphically, with each knowledge point represented by a node and dependencies between knowledge points indicated by arrows. For example, when displaying the learning sequence for applying the formula for finding the roots of a quadratic equation, the nodes are: applying the formula for finding the roots of a quadratic equation, multiplying integers, applying a linear equation, and finally a linear equation. The arrows point from back to front, clearly demonstrating the order of learning and the connections between knowledge points.

[0105] In addition to the learning sequence, the entire middle school mathematics knowledge map can also be visualized. Students can view the position of each knowledge point in the knowledge system and its extensive connection with other knowledge points. This helps students understand the structure of mathematical knowledge from a macro perspective, enhance their identification with the learning sequence, and enhance the overall planning of learning. For example, when viewing the algebra knowledge map, students can see the knowledge context from rational numbers to various equations and functions, and understand the role of the current knowledge point in the entire algebra system.

[0106] The platform provides students with multiple feedback channels, such as online questionnaires, comment sections, and dedicated feedback buttons. Students can provide feedback on their satisfaction with the learning sequence, difficulties encountered during the learning process, and suggestions for the order in which to study specific knowledge points. For example, when learning about circles in geometry according to the learning sequence, a student may find that the order of knowledge points in a certain step does not align with their usual understanding. They can inform the platform through feedback.

[0107] Based on student feedback, the system adjusts its learning sequence generation strategy. If multiple students report that the order of a knowledge point in a learning sequence is unreasonable, the system will re-analyze the dependencies of that knowledge point in the knowledge graph and the student's learning data to consider whether the learning sequence needs to be adjusted. Furthermore, if a student proposes a new learning goal (such as learning a competition-related knowledge point in advance), the system will attempt to generate a new learning sequence for the student or adjust the existing one, while still meeting the student's current learning progress and knowledge dependencies.

[0108] The platform associates each knowledge point in the learning sequence with corresponding learning resources. For example, for the knowledge point on the application of the formula for finding the roots of a quadratic equation, the associated resources include a video tutorial explaining the derivation of the formula, different types of exercises (basic, advanced, and extended), relevant simulation tests, and real-world application case studies. This allows students to easily access resources that match the current knowledge point, improving their learning outcomes.

[0109] The system also recommends personalized learning resources based on students' learning status and progress. For example, if a student demonstrates that they have learned but not mastered the application of the formula for finding the roots of a quadratic equation, the system may recommend more specialized exercises and detailed explanation videos to help them strengthen their understanding and grasp of this knowledge point.

[0110] The system records in detail the student's progress and performance as they follow the learning sequence. For each knowledge point, information is recorded, including the time the student started learning, the time to completion, the number of pauses during learning, and the accuracy rate of the exercises. For example, when learning the application of the formula for finding the roots of a quadratic equation, the system records the time from first opening the relevant learning resource to completing all recommended exercises, as well as the student's answers to the exercises.

[0111] If students encounter a point they have learned but haven't mastered during their learning process, the system will regenerate a target learning sequence. For example, if a student learns the formula for finding the roots of a quadratic equation and then performs poorly on a subsequent test, this indicates they haven't mastered that point. The system will reanalyze the knowledge graph and consider starting with other points related to the formula for finding the roots of a quadratic equation, such as reviewing the basic concepts and matching methods of quadratic equations. This will generate a new learning sequence to help students consolidate and master that point, allowing them to better advance in subsequent learning.

Claims

1. A learning sequence generation method based on learning relationship, characterized in that: The following steps are involved: Step 1: Obtain the learning status of the knowledge points in the first knowledge graph and the dependency relationship between the knowledge points, wherein the learning status includes mastered, learned but not mastered, and not learned but not mastered. If the learned knowledge point needs to rely on the mastered previous knowledge point, then there is a dependency relationship between the knowledge points; Step 2: Taking any mastered knowledge point in the first knowledge graph as the starting point, merge the mastered knowledge points that have a direct dependency relationship with it, the mastered knowledge points after merging retain the dependency relationship with the unmastered knowledge points, delete the isolated knowledge points, and generate the second knowledge graph; Step 3: From the second knowledge graph, select unlearned and unmastered knowledge points that have a direct dependency relationship with the mastered knowledge points as starting points to generate one or more first learning sequences; Step 4: If there are multiple first learning sequences, then select a first learning sequence with the longest learning path as the second learning sequence; otherwise, select a unique first learning sequence as the second learning sequence; Step 5: Starting from the last knowledge point in the second learning sequence, gradually update the knowledge points in the second learning sequence in reverse order to generate the target learning sequence; wherein, Updating the knowledge points in the second learning sequence includes: if a later knowledge point in the second sequence has multiple previous knowledge points in the second knowledge graph, merging the multiple previous knowledge points into previous knowledge points of the later knowledge point in the second sequence.

2. The learning sequence generation method based on learning relationship according to claim 1 is characterized in that: Ways to obtain the learning status of knowledge points include: automatically recording and analyzing learners' learning behavior data or learners' input through the learning system.

3. The learning sequence generation method based on learning relationship according to claim 1 is characterized in that: The basis for determining the learning status includes the learner's test scores on relevant knowledge points.

4. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: When generating the second knowledge graph, the merged and mastered knowledge points are marked to distinguish them from the unmerged knowledge points. The merge mark can be removed, and the merged and mastered knowledge points after the mark is removed can be restored.

5. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: The fourth step of "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically: if there are multiple first learning sequences with the longest learning paths, then select the first learning sequence with the most directly dependent knowledge points in the second knowledge graph as the second learning sequence.

6. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: The fourth step of "selecting a first learning sequence with the longest learning path as the second learning sequence" is specifically: if there are multiple first learning sequences with the longest learning paths, then select the first learning sequence with the least direct dependency knowledge points in the second knowledge graph as the second learning sequence.

7. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: The learning status and dependencies in the first knowledge graph are updated regularly to ensure the timeliness and accuracy of the learning sequence.

8. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: Provides a visual representation of the learning sequence.

9. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: Learners are allowed to provide feedback and evaluation on the generated learning sequences, and the system adjusts the generation strategy of the learning sequences based on the feedback.

10. The method for generating a learning sequence based on a learning relationship according to claim 1, characterized in that: The method also includes recording the learner's learning progress and performance in the process of learning according to the learning sequence, and regenerating the target learning sequence if there are knowledge points that have been learned but not mastered.

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