Learning sequence generation method based on learning relation

Abstract

The invention relates to a learning sequence generation method based on a learning relation, and belongs to the field of graph data analysis and mining. The method comprises the following steps: acquiring learning states and dependency relationships of knowledge points in a knowledge graph from a first knowledge graph, wherein the learning states comprise mastered, learned and unmastered and unlearned and unmastered; any mastered knowledge point in the first knowledge graph is used as a starting point, mastered knowledge points having a direct dependency relationship with the starting point are combined, a second knowledge graph is generated, and the dependency relationship between the combined mastered knowledge points and the non-mastered knowledge points is reserved; and from the second knowledge graph, selecting an unlearned and unmastered knowledge point which has a direct dependency relationship with the mastered knowledge point as a starting point, and generating a plurality of learning sequences. According to the method, a plurality of sequences can be dynamically generated by combining the learning state of the knowledge points and the dependency relationship between the knowledge points according to the characteristics of the mathematics subject, and a personalized efficient learning plan is formulated.

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 relations. Background Art

[0002] The learning of knowledge is an incremental process, and the learning of new knowledge depends on the knowledge that the learner has already mastered. This learning dependency relationship is manifested in that the prerequisite knowledge of a certain knowledge point must be mastered before learning the knowledge point. According to modern cognitive science theory, navigation learning based on learning dependency is an effective means to reduce cognitive load. The key issue is how to automatically generate a shortest learning sequence based on the learning dependency relationship between knowledge points and the target knowledge points that learners want to learn.

[0003] Mathematical knowledge is characterized by abstraction, precision, and logic. At the same time, mathematics learning is also the focus and difficulty of learning activities. The logic of mathematical knowledge is manifested in the strong correlation of the learning order of mathematical knowledge points. The learning path planning method in the related technology constructs a knowledge map of student learning, and plans a learning path with knowledge points as the basic unit according to 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 combine the characteristics of the mathematical subject, 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 for 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 relationship, comprising the following steps: the first step: obtaining 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 knowledge point after learning needs to rely on the previous knowledge point that has been mastered, then there is a dependency relationship between the knowledge points; the 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 the isolated knowledge points, and generating a second knowledge graph; the 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 the knowledge point is obtained by automatically recording and analyzing the learning behavior data of the learner or the input of the learner through the learning system. Thus, the present invention can update the knowledge graph and learning sequence efficiently and timely.

[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 mastered knowledge points are marked to distinguish them from the unmerged knowledge points, and the merge mark can be removed, and the merged mastered knowledge points after the mark is removed can be restored. Based on this, the second knowledge graph in the present application can be restored, thereby preventing misoperation, or making 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: 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. In this way, a learning sequence of knowledge points with more extensive associations can be constructed, which is conducive to more systematic learning of 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 updated regularly to ensure the timeliness and accuracy of the learning sequence. Thus, the learning system can more timely and accurately grasp the learner's learning status and learning plan progress, and formulate a more personalized learning strategy.

[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 according to the feedback. By accepting user feedback, the learning sequence and the learner's learning plan can be adjusted in time 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 the knowledge point on the client, which increases the convenience of using the system and thus improves the learning efficiency.

[0016] In some embodiments, the method further includes recording the learning progress and performance of the learner 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. In this way, the learning plan can be adjusted in time according to the characteristics of the learner to improve learning efficiency.

[0017] Compared with the prior art, the present invention generates an optimized learning sequence based on the learning status and dependency relationship of knowledge points in the middle school mathematics knowledge map, combined with the characteristics of mathematical knowledge. By analyzing and processing the knowledge map, starting from the knowledge points that have been mastered, the target learning sequence suitable for students to further learn is gradually derived to improve learning efficiency and effect. 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 It is a 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] In the process of learning mathematics in middle schools, students need to face many knowledge points, and there are complex dependencies between these knowledge points. Traditional learning methods often lack effective use of such dependencies, which may lead to problems such as unreasonable learning order and low learning efficiency in the learning process. The learning sequence generation method based on learning relationships proposed in this patent aims to provide a scientific and efficient learning sequence planning scheme for middle school mathematics learning, helping students to better master knowledge.

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

[0028] The knowledge system of middle school mathematics is huge, covering algebra, geometry, functions, statistics and other fields. For example, in the field of algebra, the study of linear equations is the basis for the subsequent study of systems of linear equations in two variables, quadratic equations and other contents; in geometry, the properties and theorems of triangles are the cornerstones for further study of geometric figures such as quadrilaterals and polygons. However, in the learning process, students often only study according to the order of the textbooks or the arrangements of the teachers, without fully considering the inherent dependencies between the knowledge points. This situation may cause students to learn subsequent content without fully mastering the previous knowledge points, increasing the difficulty of learning and reducing learning efficiency.

[0029] Most of the existing learning assistance tools or methods simply list and explain the knowledge points, without planning the learning sequence from the perspective of the learning status and dependency of the knowledge points. Therefore, it is necessary to develop a new method to generate a learning sequence suitable for individual students.

[0030] The core of the invention is to generate an optimized learning sequence based on the learning status and dependency relationship of knowledge points in the middle school mathematics knowledge map, combined with the characteristics of mathematical knowledge. By analyzing and processing the knowledge map, starting from the knowledge points that have been mastered, the target learning sequence suitable for students to further learn is gradually derived to improve learning efficiency and effect.

[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] The first step: obtaining the learning status of the knowledge points in the first 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.

[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 a knowledge graph at a certain moment. The first knowledge graph is generally composed of multiple knowledge points. It can be understood that in certain states, the first knowledge graph can be composed of one knowledge point. In addition, the first knowledge graph also includes the learning relationship (that is, dependency relationship) 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 students 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); if students can solve some simple linear equations, but have problems with complex questions or concept understanding, then they have learned but not mastered; if students have not yet come into contact with this knowledge point, then they have not learned or mastered it. The learning status can be represented by a flag bit of the knowledge point, for example, the learning status s=11 or 10 means mastered, the learning status s=01 means learned but not mastered, and s=00 means not learned or not mastered.

[0035] At the same time, there are rich dependencies between knowledge points. If the knowledge points to be learned later need to rely on the previous knowledge points that have been mastered, then there are dependencies between 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 a variety of ways such as analyzing textbook content, teaching syllabus, and the experience of educational experts, and obtain these learning states and dependency information from them. Dependencies 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. At this time, B is the later 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: 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 merged mastered knowledge points retain the dependency relationship with 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, "direct dependency" means direct learning relationship. Taking the first knowledge graph as an example, in the first knowledge graph, knowledge points A and C, C and D are directly dependent, while A and D are indirectly dependent. "Isolated knowledge points" refer to knowledge points that have no dependency relationship with other knowledge points, that is, the learning of this knowledge point does not need to rely on the learning or mastering of other knowledge points, and the learning or mastering of other knowledge points does not rely on the mastering or learning of this knowledge point as a prerequisite.

[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 in the figure, 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, then the knowledge graph after the second step is as follows Figure 3 shown.

[0043] Assume that in the knowledge graph of the algebra section of middle school mathematics, the knowledge point that has been mastered is a linear equation, which has a direct dependency relationship with a system of linear equations with two variables (because the substitution elimination method and the addition and subtraction elimination method for solving a system of linear equations with two variables are related to the solution of a linear equation with one variable), and a linear equation with one variable also has a dependency relationship with a linear inequality with one variable (the steps for solving a linear inequality with one variable are similar to those for a linear equation with one variable). We take the linear equation with one variable as the starting point, merge the system of linear equations with two variables and linear inequality with one variable, which are the knowledge points that have been mastered, retain the dependency relationship between them and the knowledge points that have not been mastered (such as a system of linear equations with three variables, whose solution is related to the system of linear equations with two variables, and it is currently assumed that students have not mastered it), delete those isolated knowledge points (such as an ancient mathematical algorithm knowledge point that is not related to the currently mastered and related unmastered knowledge points), and thus generate 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 in 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] The third step: From the second knowledge graph, select unlearned and unmastered knowledge points that have a direct dependency on the mastered knowledge points as the starting point, and generate one or more first learning sequences.

[0046] After the previous step, the second knowledge graph obtained has been greatly simplified, and multiple first learning sequences will be obtained through this step. In this step, unlearned and unmastered knowledge points that have a direct dependency relationship with the mastered knowledge points are selected as the starting point of the learning sequence. For knowledge points that have been learned but not mastered, it is not appropriate to use them as the starting point of the learning sequence. This can improve the efficiency of learning 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 relationship with the 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 should be noted that if the learning of an unlearned and unmastered knowledge point does not need to rely on the mastered knowledge point, then the node is regarded as an unlearned and unmastered knowledge point that has a direct dependency relationship with the mastered knowledge point. It is understandable that this type of knowledge point actually also has a mastered knowledge point with a direct dependency relationship, but it is not shown on the knowledge graph. Taking the second knowledge graph as an example, if knowledge point B is an unlearned and unmastered knowledge point, then this knowledge point can be used as the starting point of the learning sequence.

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

[0049] From the second knowledge graph, take the unlearned and unmastered knowledge points that have a direct dependency relationship with the mastered knowledge points as the starting point. For example, starting from a system of linear equations, a learning sequence can be generated based on the dependency relationship: a system of linear equations → a system of linear equations → a system of linear equations. At the same time, if there are other unlearned and unmastered knowledge points, such as a quadratic function (which has a dependency relationship with a linear equation in terms of the connection between functions and equations), another learning sequence can be generated: a system of linear equations → a quadratic function. In this way, multiple first learning sequences are generated.

[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] Among the generated multiple first learning sequences, their learning path lengths are compared. Assuming that the first learning sequence mentioned above has 3 knowledge points and the second learning sequence has 2 knowledge points, then the first learning sequence (one-variable linear equation system → two-variable linear equation system → three-variable linear equation) is selected 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 the related art, a learning sequence with a shorter learning path tends to be selected, while in this case, a longer learning sequence is selected. Mathematical knowledge has the characteristics of high learning difficulty, strong logic, strong knowledge coherence and relevance. Combined with the characteristics of the mathematical subject, choosing a learning sequence with a longer path can provide learners with motivational feedback in a timely manner and enhance learners' interest in learning. At the same time, a learning sequence with a longer learning path can combine as many knowledge points as possible, establish a learning logic with basic knowledge points as the main line, connect the knowledge points of the entire middle school mathematics, and establish learners' framework 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: 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. In this way, a learning sequence of knowledge points with more extensive associations can be constructed, which is conducive to more systematic learning of 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 FIG. 1 is a schematic diagram of a 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] The fifth step: taking the last knowledge point in the second learning sequence as the starting point, gradually and reversely update the knowledge points in the second learning sequence to generate a target learning sequence; wherein, updating the knowledge points in the second learning sequence includes: if there are multiple previous knowledge points for the latter knowledge point in the second sequence in the second knowledge graph, then merging the multiple previous knowledge points into the previous knowledge point of the latter knowledge point in the second sequence.

[0057] Figure 8It 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, so in the updating process, knowledge point G, knowledge point F and knowledge point H are merged into one knowledge point GFH, and the target learning sequence B→ACD→E→GFH→I is obtained after the update, so that the learning sequence has more knowledge points and is more conducive to the systematic mastery of knowledge.

[0058] Starting from the last knowledge point (linear equation) in the second learning sequence, update in reverse order step by step. In the second knowledge graph, there are knowledge points with direct dependency on linear equations and inequality-related knowledge points (such as linear inequalities). Then merge the linear inequalities as the previous knowledge point of the linear equations. The updated learning sequence becomes: linear inequality + linear equation → two-variable linear equation group → three-variable linear equation group. Continue to update in reverse order. If it is found that there is also inequality group-related knowledge related to the linear inequality (assuming it has not been considered before), continue to merge and finally generate the target learning sequence. This target learning sequence can help students start from the knowledge they have mastered and systematically learn related knowledge that they have not mastered, and fully consider the dependency between knowledge points.

[0059] This embodiment is carried out on an online learning platform for middle school mathematics. The platform has a complete database of middle school mathematics knowledge, including detailed explanations of each knowledge point, examples, exercises, etc. At the same time, the platform can record each student's learning of the knowledge point, and comprehensively judge the learning status of the knowledge point through various data such as the student's practice results, test scores, and study time.

[0060] Figure 6 Schematic diagram of an online learning platform in some embodiments of the present application. Figure 6 As shown, the learning system in this case includes learners, a server, and multiple clients. Learners learn through the learning interface provided by the client, the client records the learner's learning behavior, and 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 main users of this learning system. They acquire knowledge and improve their skills by accessing the system. The client presents an intuitive and easy-to-use learning interface to learners. This interface is designed to be concise and easy to operate, so that learners can quickly find the required learning resources, such as course catalogs, learning materials, etc. For example, the interface may display courses of different subjects and different difficulty levels in the form of a classified menu, and learners can easily click to enter the course page of interest. In the process of learners using the learning interface to learn, the client can record the learners' various learning behaviors in detail. These behaviors include but are not limited to the learners' access time, stay time, learning order, answering of questions (if there are exercises or tests), pause and replay times of video playback, etc. For example, when a learner is watching a math course video, the client will record the time when he pauses the video at a certain knowledge point, and whether the part of the content is replayed later, which can reflect the difficulty of the learner's understanding of the knowledge point.

[0062] The server is responsible for receiving learners' learning behavior data from various clients. It uses advanced data processing algorithms to analyze and process these data. For example, for learners' answer data, the server can determine which knowledge points the learners have a low accuracy rate and which knowledge points they have mastered better. For learning time data, the server can analyze the time trend of learners in different types of courses to understand learners' learning preferences. The processed data will be fed back to learners through the client again. For example, after the server analyzes that the learner has a weak link in a certain sub-item of English grammar, it will push targeted learning suggestions to the learner through the client, such as related special exercises, supplementary materials, or recommend other courses that explain the knowledge point in more depth. At the same time, it will also show learners their overall performance trends in the learning process, such as the completion of learning progress, changes in learning efficiency, etc., to help learners better understand their learning status.

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

[0064] The application layer is the most direct level for the learning system to interact with learners and clients. It is responsible for presenting various learning functions and services to learners, such as course management, learning plan formulation, and learning achievement display. For example, learners can set their own learning goals and plans at the application layer, and the application layer will generate personalized learning path recommendations for learners based on these settings, and track the execution of the plan during the learning process, reminding learners to complete various learning tasks.

[0065] The computing layer undertakes the main computing tasks in the system. It uses powerful computing power to conduct in-depth mining and analysis of learning data. For example, it uses complex algorithms to calculate the similarity between learners so as to recommend courses or learning methods chosen by other learners with similar learning patterns and good learning results. At the same time, the computing layer is also responsible for processing various model operations in the learning system, such as building personalized learning models based on learners' historical learning data, and predicting the difficulties and learning effects that learners may encounter in different learning scenarios.

[0066] The communication interface layer ensures stable and efficient communication between the server and each client. It can handle a large amount of concurrent data transmission. Whether the learner's operation data on the client is uploaded to the server, or the feedback data processed by the server is transmitted to the client, the communication interface layer can ensure the integrity and timeliness of the data. For example, during high-concurrency learning peak hours, such as at night or on weekends, the communication interface layer can ensure that the data interaction between each client and the server is not affected through optimized communication protocols and data caching mechanisms, and the learner's learning experience remains smooth.

[0067] The database is the data storage center of the entire learning system. It stores a large amount of learning resource information, including videos, documents, audio materials, etc. of various courses, as well as personal information, learning history data, learning behavior records, etc. of all learners. For example, when a learner needs to revisit a course he has studied before, the database can quickly and accurately call up relevant course materials and the learner's learning progress in the course, providing support for the learner's continuous learning. In addition, the database will regularly perform data backup and optimization to ensure data security and efficient operation of the system.

[0068] The middle school mathematics knowledge map covers all the mathematics content from the first to the third grade of junior high school. Taking the algebra part as an example, it includes numbers and expressions (rational numbers, irrational numbers, integers, fractions, etc.), equations and inequalities (linear equations of one variable, systems of linear equations of two variables, quadratic equations of one variable, linear inequalities of one variable, etc.), functions (linear functions, quadratic functions, inverse proportional functions, etc.). The geometry part includes triangles (properties of triangles, congruent triangles, similar triangles, etc.), quadrilaterals (parallelograms, rectangles, rhombuses, squares, etc.), circles, etc. There are also knowledge points in statistics and probability, such as data collection and organization, probability calculation, etc.

[0069] In algebra, the operation rules of rational numbers are the basis of the operation of whole expressions, because the coefficients in whole expressions are all rational numbers, and the proficiency of addition, subtraction, multiplication and division of rational numbers will affect the operation of whole expressions. For example, in the addition operation of whole expressions, the coefficients (rational numbers) of the same terms need to be added.

[0070] For the equation part, the linear equation of one variable is the basis of the system of linear equations of two variables. The method of elimination is to express an unknown number with an equation containing another unknown number, and then substitute it into another equation to achieve elimination. This process involves solving the linear equation of one variable.

[0071] In geometry, the triangle interior angle theorem is the basis for the derivation of 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 part, the graph of a linear function is a straight line, and the concepts of its slope and intercept are closely related to the coefficients of a linear equation. To solve the coordinates of the intersection of a linear function and the coordinate axis, we just need to set or, which is transformed into solving a linear equation.

[0073] In the statistics and probability section, the collection and organization of data is the basis for calculating probability. Only by accurately collecting and organizing data can we correctly calculate the frequency of events and then estimate the probability.

[0074] For each student, the platform determines the learning status of a knowledge point according to the following methods: Mastered: If the student's accuracy rate in the exercises related to this knowledge point reaches more than 90%, and in the most recent chapter test, all the questions related to this knowledge point are correct, and the cumulative time of learning this knowledge point exceeds a certain threshold (set according to the difficulty of the knowledge point, such as 1 hour for simple knowledge points and 3 hours for complex knowledge points), then it is judged to have mastered it.

[0075] 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 learning time reaches a certain level (such as 0.5 hours for simple knowledge points and 2 hours for complex knowledge points).

[0076] 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 very short (lower than the time threshold set above), it will be judged as not learned and not mastered.

[0077] The first step is to perform an example. Taking the student learner as an example, the platform obtains information from his knowledge graph. In the algebra part, the learner's learning status for the linear equation is mastered, and the learning status for the quadratic equation is learned but not mastered (he can solve some simple quadratic equations, but often makes mistakes when using Vieta's theorem to solve problems). For higher-order equations (such as cubic equations), he is in a state of not learning and not mastering. In the geometry part, the learner has mastered the properties of triangles, has learned but not mastered the determination theorem of similar triangles (sometimes confusing different determination methods), and has not learned or mastered the relevant knowledge of circles.

[0078] At the same time, the platform clarifies the dependencies between knowledge points. For example, in algebra, the solution methods of quadratic equations (matching method, formula method, etc.) are dependent on operations such as transposition and formula of linear equations; in geometry, the determination of similar triangles is dependent on the internal angle theorem of triangles and the proportional relationship of sides.

[0079] Example of executing the second step. Assume that the knowledge points that the learner has mastered in the algebra part include linear equations and multiplication of integers. The platform takes the linear equation as the starting point and finds that it has a direct dependency with the multiplication of integers (the multiplication of integers may be involved in the step of removing the denominator of solving the linear equation), and merges them. At the same time, delete those 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 the current middle school mathematics learning and subsequent learning), and generate 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.

[0080] Example of executing the third step. From the newly generated second knowledge graph, select the unlearned and unmastered knowledge points that have a direct dependency on the mastered knowledge points as the starting point. For learners, in the algebra part, starting with the factorization method for solving quadratic equations, generate a first learning sequence: linear equations (consolidation) → multiplication of integers (review) → factorization method for solving quadratic equations. If there are other unlearned and unmastered knowledge points, such as fractional equations (the step of removing the denominator in the solution process is related to the multiplication of integers), another learning sequence can be generated: fractional equations → multiplication of integers → linear equations. In this way, multiple first learning sequences are generated for learners in the algebra part.

[0081] The fourth step is to perform an example. Compare the learning path lengths of these first learning sequences. Assume that the first learning sequence has 3 knowledge points and the second learning sequence has 3 knowledge points (this is just an example and may be different in practice). Further compare the depth of association and coverage between knowledge points. If the first learning sequence is more comprehensive in reviewing and consolidating related knowledge (for example, it involves more types of review of integer multiplication and the application of linear equations in factorization), then select the first learning sequence as the second learning sequence.

[0082] Example of executing the fifth step. Starting from the last knowledge point (linear equation) in the second learning sequence, update in reverse order step by step. In the second knowledge graph, it is found that there are also knowledge points of application of linear equations (such as travel problems, engineering problems, etc.) that are directly dependent on linear equations. The application knowledge points of linear equations are merged as the previous knowledge points of linear equations. The updated learning sequence becomes: factorization method for solving quadratic equations → multiplication of integers → application of linear equations → linear equations. Continue to update in reverse order. If it is found that there are also knowledge points of quantitative relationship analysis in practical problems related to the application of linear equations, continue to merge, and finally generate a target learning sequence suitable for the learner, helping him to learn the factorization method for solving quadratic equations more efficiently based on the knowledge he has mastered, while consolidating the relevant basic knowledge and related knowledge.

[0083] For students who are about to learn a new chapter, such as the chapter on circles in the third grade of junior high school, the platform generates a preview learning sequence using the method of the present invention based on the students' previous mastery of geometric knowledge (such as the mastery of relevant knowledge such as triangles and quadrilaterals). Starting from the basic geometric knowledge that has been mastered, the dependency relationship of knowledge points related to circles is found, and a learning sequence is generated, so that students can understand the connection between circles and previous knowledge in a targeted manner during the preview process, and better understand new content.

[0084] During the final exam review stage, for students who have a poor grasp of overall algebra knowledge, the platform generates a review learning sequence based on the students' learning status in various algebra knowledge points (from numbers and expressions to equations and inequalities, functions, etc.). For example, starting from the mastered linear equations, through the knowledge graph and dependency relationships, the review order of the entire algebra part is sorted out, and which knowledge points to review first can better help understand and consolidate other knowledge points and improve the review efficiency.

[0085] For students who have spare time and want to expand their mathematical knowledge, the platform can generate a learning sequence based on the dependency between the extended part of the middle school mathematics knowledge map (such as competition mathematics related knowledge points) and the normal teaching knowledge points. For example, starting from the function knowledge they have mastered, a learning sequence is generated for students to guide them to learn advanced knowledge of functions, such as function iteration, fixed points and other competition-related content, to help students gradually expand their knowledge.

[0086] By comparing the time it takes for students to complete 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 (such as reduced by more than 20%) after using this method, it means that the learning efficiency has been significantly improved.

[0087] By analyzing the students' scores in the exercises and tests related to the knowledge points, if the students' accuracy rate in the tests related to the knowledge points is significantly improved (for example, by more than 15%) after learning using the learning sequence generated by this method, it means that the students' mastery of the knowledge points has been improved.

[0088] By analyzing the matching degree between the learning path of students in the learning process and the dependency relationship of knowledge points in the knowledge graph, if the learning path of students is highly consistent with the dependency relationship (for example, the learning order of more than 80% of the knowledge points conforms to the dependency relationship), then the learning path is reasonable.

[0089] After a one-semester experiment on 100 middle school students, it was found that the 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 about 25%. In terms of the mastery of knowledge points, the test scores increased by about 20% on average. At the same time, the analysis of students' learning paths showed that about 85% of the students' learning paths matched the dependencies in the knowledge graph well, indicating that the learning sequence generation method of the present invention has a good application effect in middle school mathematics learning.

[0090] 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. Whether in learning scenarios such as preview, review or knowledge expansion, it has a good application effect, providing 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 extended to other subject areas to provide stronger support for students' comprehensive learning.

[0091] In some embodiments, the learning status of the knowledge point is obtained by automatically recording and analyzing the learning behavior data of the learner or the input of the learner through the learning system. Thus, the present invention can update the knowledge graph and learning sequence efficiently and timely.

[0092] 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.

[0093] In some embodiments, when generating the second knowledge graph, the merged mastered knowledge points are marked to distinguish them from the unmerged knowledge points, and the merge mark can be removed, and the merged mastered knowledge points after the mark is removed can be restored. Based on this, the second knowledge graph in the present application can be restored, thereby preventing misoperation, or making adjustments based on human settings.

[0094] In some embodiments, in the fourth step "Fourth step: 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 path, then select one of the first learning sequences with the most knowledge points directly dependent on the first sequence as the second learning sequence. In this way, a learning sequence of knowledge points with more extensive associations can be constructed, which is conducive to more systematic learning of learners.

[0095] In some embodiments, in the fourth step "Fourth step: 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 path, then select one of the first learning sequences with the least direct dependency relationship with the first sequence as the second learning sequence. In this way, a more lightweight learning sequence of knowledge points can be constructed, which is conducive to learners mastering knowledge more quickly.

[0096] In some embodiments, the learning status and dependencies in the first knowledge graph are updated regularly to ensure the timeliness and accuracy of the learning sequence. Thus, the learning system can more timely and accurately grasp the learner's learning status and learning plan progress, and formulate a more personalized learning strategy.

[0097] In some embodiments, a visual display of the learning sequence is provided, which can improve the usability and friendliness of the system.

[0098] 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 according to the feedback. By accepting user feedback, the learning sequence and the learner's learning plan can be adjusted in time to improve learning efficiency.

[0099] 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 the knowledge point on the client, which increases the convenience of using the system and thus improves the learning efficiency.

[0100] In some embodiments, the method further includes recording the learning progress and performance of the learner 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. In this way, the learning plan can be adjusted in time according to the characteristics of the learner to improve learning efficiency.

[0101] The knowledge graph update mechanism in this case. As students progress in their studies, the learning status and dependencies in the knowledge graph may change. For example, the update of textbook content may lead to adjustments in the dependencies between knowledge points, or students’ learning status may change after relearning a certain knowledge point. Therefore, updating the first knowledge graph regularly (such as weekly or monthly) is the key to ensuring the timeliness and accuracy of the learning sequence.

[0102] When updating the learning status, the system re-analyzes the student's data in recent learning activities, including new practice results, test scores, and changes in learning time. For updates to dependencies, the platform will refer to the advice of education experts, new teaching outlines, and the latest textbook content. For example, if the new textbook adjusts the teaching order of functions, or adds content related to functions and other knowledge points, the system will modify the dependencies in the knowledge graph accordingly to ensure that the subsequent generated learning sequence meets the latest teaching requirements.

[0103] The platform provides students with a visual display interface for learning sequences. The learning sequence is presented in a graphical way, with each knowledge point represented by a node and the dependencies between knowledge points represented by arrows. For example, when showing the learning sequence of the application of the formula for finding the roots of a quadratic equation, the nodes are the application of the formula for finding the roots of a quadratic equation, multiplication of integers, practical application of a linear equation, and a linear equation. The direction of the arrows is from back to front, clearly showing the order of learning and the relationship between knowledge points.

[0104] 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 their extensive connections with other knowledge points. This helps students understand the structure of mathematical knowledge from a macro perspective, enhance their sense of identity with the learning sequence and the planning of overall 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.

[0105] The platform provides students with multiple feedback channels, such as online questionnaires, comment areas, 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 certain knowledge points should be learned. For example, when students are learning about circles in geometry according to the learning sequence, they may find that the order of knowledge points in a certain step does not quite match their own understanding habits, and they can inform the platform through feedback.

[0106] Based on students' feedback, the system adjusts the generation strategy of learning sequences. 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 the knowledge point in the knowledge graph and the students' learning data to consider whether the learning sequence needs to be adjusted. At the same time, if students propose new learning goals (such as learning a competition-related knowledge point in advance), the system will try to generate a new learning sequence for the student or adjust the existing learning sequence on the premise of meeting the current learning progress and knowledge dependencies.

[0107] The platform associates each knowledge point in the learning sequence with the corresponding learning resources. For the knowledge point of applying the formula for finding the roots of quadratic equations, the associated resources include video tutorials that explain the derivation process of the formula, different types of exercises (basic questions, advanced questions, and extended questions), related simulation test questions, and actual application case analysis. In this way, students can easily obtain resources that match the current learning knowledge points during the learning process, improving their learning effect.

[0108] The system will also recommend personalized learning resources based on the student's learning status and progress. If a student shows that he has learned but not mastered the application knowledge point of the formula for finding the roots of a quadratic equation, the system may recommend more special exercises and detailed explanation videos to help students strengthen their understanding and mastery of this knowledge point.

[0109] The system records in detail the learning progress and performance of students in the learning process according to the learning sequence. For each knowledge point, it records the time when students start learning, the time when they finish learning, the number of pauses during the learning process, the accuracy of the exercises, etc. For example, when learning the application knowledge point of the formula for finding the roots of a quadratic equation, it records the time span from the first opening of the relevant learning resources to the completion of all recommended exercises, as well as the answers to the exercises.

[0110] If students have learned but not mastered knowledge points during the learning process, the system will regenerate the target learning sequence. For example, after learning the application of the formula for finding the roots of a quadratic equation, students did not perform well in the subsequent test, indicating that they did not master the knowledge point. The system will re-analyze the knowledge graph and consider starting with other knowledge points related to the application of the formula for finding the roots of a quadratic equation, such as reviewing the basic concepts and matching methods of quadratic equations, and generate a new learning sequence to help students consolidate and master the knowledge point again, so as to better promote 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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