CN119336823B

CN119336823B - Learning sequence generation method based on learning relation

Info

Publication number: CN119336823B
Application number: CN202411907537.6A
Authority: CN
Inventors: 严汝建; 杨玉德
Original assignee: Shandong Shunshi Education Technology Group Co ltd
Current assignee: Shandong Shunshi Education Technology Group Co ltd
Priority date: 2024-12-24
Filing date: 2024-12-24
Publication date: 2025-04-15
Anticipated expiration: 2044-12-24
Also published as: CN119336823A

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

Learning sequence generation method based on learning relation

Technical Field

The invention relates to the field of graph data analysis and mining, in particular to a learning sequence generation method based on a learning relationship.

Background

Learning of knowledge is an increasing process, and learning of new knowledge depends on knowledge that a learner has mastered. This learning dependency is manifested in that the knowledge points must be mastered before learning them. According to modern cognitive science theory, navigation learning based on learning dependency relationship is an effective means for reducing cognitive load. The key problem is how to automatically generate a shortest learning sequence according to the learning dependency relationship among knowledge points and the target knowledge points to be learned by the learner.

Mathematical knowledge has the characteristics of abstraction, accuracy and logic. Meanwhile, mathematical learning is also an important point and a difficult point in learning activities, and the logic property of mathematical knowledge is represented by strong relevance to the learning sequence of mathematical knowledge points. According to the learning path planning method in the related technology, a learning path taking a knowledge point as a basic unit is planned according to the learning dependency relationship of the knowledge point by constructing a knowledge map learned by students, so that the shortest generated learning sequence is realized. However, the planning of this type of method is static, the planned path is also unreasonable, and the method is difficult to implement without combining the characteristics of mathematical disciplines.

Disclosure of Invention

In order to solve the problems in the prior art, the invention discloses a learning sequence generation method based on learning dependency relationships, which can dynamically plan and adjust the learning sequence of mathematical knowledge while meeting the learning dependency relationships aiming at knowledge points to be learned by learners, thereby improving the learning efficiency.

In order to achieve the above purpose, the technical scheme adopted by the invention is a learning sequence generation method based on a learning relation, comprising the following steps of acquiring a learning state of a knowledge point in a first knowledge map and a dependency relation between knowledge points from the first knowledge map, wherein the learning state comprises the learned and learned non-learned and non-learned, if the learned knowledge points need to depend on the learned front knowledge points, the dependency relation exists between the knowledge points, the second step takes any one of the learned knowledge points in the first knowledge map as a starting point, combines the learned knowledge points with the direct dependency relation, the combined learned knowledge points retain the dependency relation with the non-learned knowledge points, the second knowledge map is generated, the third step selects the non-learned knowledge points with the direct dependency relation with the learned knowledge points from the second knowledge map as the starting point, and generates one or more first learning sequences, the fourth step selects a first learning sequence with the longest learning path from the first learning sequence if the learned front knowledge points need to depend on the learned front knowledge points, and the second step takes the learned front knowledge points in the second learning sequence as the second learning sequence, and if the learned front knowledge points in the first learning sequence have the second learning sequence have the longest learning path, and the first learning sequence is the first learning sequence and the first learning sequence has the first learning sequence with the highest learning sequence.

In some embodiments, the manner in which the learning state of the knowledge points is obtained includes automatically recording and analyzing, by the learning system, learning behavior data of the learner, or input by the learner. Therefore, the invention can efficiently and timely update the knowledge graph and the learning sequence.

In some embodiments, the determination of the learning state is based on test performance of the learner at the relevant knowledge point. The learning state of the learner to the knowledge points can be accurately detected through the test results.

In some embodiments, when the second knowledge graph is generated, the merged mastered knowledge points are marked to be different from the knowledge points which are not merged, the merged mark can be removed, and the merged mastered knowledge points after the mark removal can be restored. Based on this, the second knowledge graph in the present application can be restored, and thus erroneous operation can be prevented, or adjustment can be performed based on artificial settings.

In some embodiments, the fourth step, namely the first learning sequence with the longest learning path is selected as the second learning sequence in the fourth step, specifically, if a plurality of first learning sequences with the longest learning path exist, the first learning sequence with the most direct dependency knowledge points in the second knowledge graph is selected as the second learning sequence. Therefore, a learning sequence of knowledge points with wider association can be constructed, and the learner can learn more systematically.

In some embodiments, the "one first learning sequence with the longest learning path is selected as the second learning sequence in the fourth step" specifically, if there are a plurality of first learning sequences with the longest learning path, the first learning sequence with the least direct dependency knowledge points in the second knowledge graph is selected as the second learning sequence.

Therefore, a lighter learning sequence of knowledge points can be constructed, and a learner can master knowledge more quickly.

In some embodiments, the learning states and dependencies in the first knowledge-graph are updated periodically to ensure timeliness and accuracy of the learning sequence. Therefore, the learning system can more timely and accurately master the learning state and the learning plan progress of the learner, and a more personalized learning strategy is formulated.

In some embodiments, a visual presentation of the learning sequence is provided. Through visual display, the usability and the friendliness of the system can be improved.

In some embodiments, the learner is allowed to feedback and evaluate the generated learning sequence, and the system adjusts the generation strategy of the learning sequence based on the feedback. By receiving feedback from a user, the learning sequence and the learning plan of the learner can be timely adjusted, and the learning efficiency is improved.

In some embodiments, a learning sequence is associated with a learning resource. Through correlating the learning sequence with the learning resources, a learner can timely acquire the learning resources by clicking the knowledge points on the client, so that the convenience of system use is improved, and the learning efficiency is improved.

In some embodiments, the method further includes recording a learning progress and performance of the learner during learning according to the learning sequence, and regenerating the target learning sequence if learning of the non-learned knowledge points occurs. Therefore, the learning plan can be timely adjusted according to the characteristics of learners, and the learning efficiency is improved.

Compared with the prior art, the method and the device generate the optimized learning sequence according to the learning state and the dependency relationship of the knowledge points in the mathematical knowledge graph of the middle school and combining the characteristics of the mathematical knowledge. By analyzing and processing the knowledge graph, a target learning sequence suitable for students to learn further is deduced step by step from the mastered knowledge points, so that learning efficiency and effect are improved.

Drawings

FIG. 1 is a schematic diagram of a learning sequence generation process based on learning relationships in some embodiments of the application.

Fig. 2 is a schematic diagram of a first knowledge-graph in some embodiments of the application.

Fig. 3 is a schematic diagram of a second knowledge-graph in some embodiments of the application.

Fig. 4 is a schematic diagram of a plurality of first learning sequences in some embodiments of the application.

Fig. 5 is a schematic diagram of a second learning sequence in some embodiments of the application.

Fig. 6 is a schematic diagram of an online learning platform in some embodiments of the application.

Fig. 7 is a schematic diagram of a learning system in some embodiments of the application.

FIG. 8 is a target learning sequence in some embodiments of the application.

Detailed Description

In the middle school mathematics learning process, students need to face numerous knowledge points, and complex dependency relationship exists among the knowledge points. The traditional learning mode often lacks effective utilization of the dependency relationship, so that the problems of unreasonable learning sequence, low learning efficiency and the like of students in the learning process can occur. The learning sequence generation method based on the learning relation provided by the invention aims to provide a scientific and efficient learning sequence planning scheme for mathematics learning in middle schools and helps students to master knowledge better.

The invention relates to the technical field of education, in particular to a learning sequence generation method based on a learning relationship, which is applied to middle school mathematics learning.

The mathematical knowledge system of middle school is huge and covers a plurality of fields such as algebra, geometry, functions, statistics and the like. For example, in the algebraic field, the learning of the unified first-order equation is the basis for the subsequent learning of the contents of the binary first-order equation set, the unified second-order equation, etc., and in the geometry, the nature and theorem of the triangle are the basis for further learning geometric figures such as quadrilaterals, polygons, etc. However, students often learn only according to the order of teaching materials or the arrangement of teachers in the learning process, and the inherent dependency relationship between knowledge points is not fully considered. This situation may lead to students learning subsequent content without fully mastering the pre-knowledge points, increase learning difficulty, and reduce learning efficiency.

Most of the existing learning auxiliary tools or methods simply list and explain knowledge points, and the learning sequence is not planned from the learning state and the dependency relation of the knowledge points. Therefore, there is a need to develop a new method to generate learning sequences suitable for individual situations of students.

The core of the invention is to generate an optimized learning sequence according to the learning state and the dependency relationship of knowledge points in a middle school mathematic knowledge map and combining the characteristics of mathematic knowledge. By analyzing and processing the knowledge graph, a target learning sequence suitable for students to learn further is deduced step by step from the mastered knowledge points, so that learning efficiency and effect are improved.

FIG. 1 is a schematic diagram of a learning sequence generation process based on learning relationships in some embodiments of the application. As shown in fig. 1, the present method includes 5 basic steps.

The first step is to acquire learning states of knowledge points in a first knowledge graph and dependency relations among the knowledge points from the first knowledge graph, wherein the learning states comprise mastered, learned and unlearned.

Fig. 2 is a schematic diagram of a first knowledge-graph in some embodiments of the application. As shown in fig. 2, the first knowledge-graph is an initial graph at a certain moment, and the first knowledge-graph may be a reconstructed graph or a knowledge-graph of a certain knowledge-graph at a certain moment. The first knowledge-graph is generally composed of a plurality of knowledge points, and it is understood that in some states, the first knowledge-graph may be composed of one knowledge point. In addition, the first knowledge graph also includes learning relationships (i.e., dependency relationships) between knowledge points.

In the middle school mathematics knowledge graph, each knowledge point has a unique learning state. For example, for a knowledge point, if a student can proficiently solve various types of unified equations and understand their concepts and applications, the learning state of this knowledge point is mastered (knowledge points that have been mastered without learning are included), if a student can solve some simple unified equations but there is a problem in complex question type or concept understanding, it is learned without mastering, and if a student has not contacted this knowledge point, it is not learned without mastering. For the learning state, it may be indicated by one flag bit of the knowledge point, for example, learning state s=11 or 10 indicates mastered, learning state s=01 indicates learned not mastered, and s=00 indicates not learned not mastered.

Meanwhile, rich dependency relations exist among knowledge points, and if the learned knowledge points need to depend on the mastered previous knowledge points, the knowledge points have the dependency relations. Taking function knowledge as an example, the learning of the primary function depends on the knowledge of the unitary primary equation, because the expression of the primary function is closely related to the unitary primary equation, and a solution of the unitary primary equation is needed when solving the problems of the intersection point of the primary function and the coordinate axis, and the like. The learning state and the dependency relationship information can be obtained by constructing a middle school mathematic knowledge graph through various ways of analyzing the content of teaching materials, the outline of teaching, the experience of education specialists and the like. For the dependency relationship, a "→" expression, for example, an a→b expression may be used, and learning of the knowledge point B is premised on grasping the knowledge point a, where B is a rear knowledge point and a is a front knowledge point.

It will be appreciated that the learning state represents the characteristics of each knowledge point itself, and the dependency relationship is the relationship between the knowledge point and other knowledge points.

The purpose of this step is to acquire the learning relationship between the knowledge points and the grasp state of the current learner with respect to the knowledge points, so as to facilitate the operation of the subsequent step.

And the second step is to use any one of the grasped knowledge points in the first knowledge graph as a starting point, combine the grasped knowledge points with direct dependency relationship, reserve the dependency relationship between the grasped knowledge points after combination and the non-grasped knowledge points, delete the isolated knowledge points and generate a second knowledge graph.

The aim of this step is to simplify the knowledge graph. The knowledge graph can be simplified by combining the mastered knowledge points and deleting the isolated knowledge points, so that the knowledge graph is clearer and the subsequent processing is convenient.

In the present case, the "direct dependency relationship" is a 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 direct dependency relationships, and a and D are indirect dependency relationships. The "isolated knowledge point" refers to a knowledge point that has no dependency on other knowledge points, that is, learning of the knowledge point does not need to depend on learning or mastering of other knowledge points, and learning or mastering of other knowledge points is not premised on learning or mastering of the knowledge point.

In this case, for knowledge points having a direct dependency relationship, for example, knowledge point F and knowledge point I, learning of knowledge point I depends on learning of knowledge point F, so knowledge point F is referred to as a front knowledge point of knowledge point I, knowledge point I is referred to as a rear knowledge point of knowledge point F, and it should be noted that the front knowledge and the rear knowledge point are not necessarily unique, for example, knowledge point I has a plurality of front knowledge points, and knowledge point B has a plurality of rear knowledge points.

Fig. 3 is a schematic diagram of a second knowledge-graph in some embodiments of the application. As shown in fig. 2-3, assuming that the knowledge points A, C, D are grasped knowledge points and J is an isolated knowledge point in the first knowledge map, the knowledge map after the second step is shown in fig. 3.

It is assumed that in the knowledge graph of the algebraic part of mathematics in middle school, the grasped knowledge point is a unitary one-time equation which has a direct dependency relationship with the binary one-time equation set (because the substitution and addition and subtraction of solving the binary one-time equation set are both related to the solution of the unitary one-time equation), and the unitary one-time equation and the unitary one-time inequality also have a dependency relationship (the step of solving the unitary one-time inequality is similar to the unitary one-time equation). The first knowledge map is generated by taking a unified first-order equation as a starting point, combining the mastered knowledge points of the binary first-order equation set and the unified first-order inequality, reserving the dependency relationship between the mastered knowledge points and the unconsolidated knowledge points (such as the ternary first-order equation set, the solution of which is associated with the binary first-order equation set to a certain extent and the fact that students do not master at present), and deleting the isolated knowledge points (such as certain ancient mathematical algorithm knowledge points which are not associated with the currently mastered and related unconsolidated knowledge points).

All the knowledge points which are mastered in a certain area in the knowledge graph are changed into one mastered knowledge point by merging the mastered knowledge points which directly have the dependency relationship one by one, and meanwhile, the dependency relationship between the mastered knowledge points after merging and the knowledge points which are not mastered is reserved, so that the subsequent processing is convenient.

And thirdly, selecting unlearned knowledge points with direct dependency relationship with the mastered knowledge points from the second knowledge graph as starting points, and generating one or more first learning sequences.

The second knowledge graph obtained after the previous step has been greatly simplified, and a plurality of first learning sequences will be obtained through this step. In the step, the unlearned knowledge points with direct dependency relationship with the mastered knowledge points are selected as the starting points of the learning sequence, and the learned unlearned knowledge points are not suitable to be used as the starting points of the learning sequence, so that the learning efficiency can be improved, and excessive time waste on one knowledge difficulty point is avoided. Meanwhile, the un-learned and un-mastered knowledge points which have no direct dependency relationship with the mastered knowledge points are not suitable to be used as the starting points of the learning sequence, and the knowledge points are used as the middle nodes or the end nodes of the learning sequence.

Note that if learning of one unlearned knowledge point does not need to depend on the learned knowledge point, the node is regarded as an unlearned knowledge point having a direct dependency relationship with the learned knowledge point. It will be appreciated that the knowledge points of this type also actually have knowledge points that are known to be directly dependent, but are not shown on the knowledge graph. Taking the second knowledge graph as an example, if the knowledge point B is a learning-free knowledge point, the knowledge point B may be used as a starting point of the learning sequence.

Fig. 4 is a schematic diagram of a plurality of first learning sequences in some embodiments of the application. As shown in fig. 4, starting from the knowledge point B, 4 first learning sequences can be obtained, some learning sequences having 4 knowledge points and some learning sequences having 5 knowledge points.

From the second knowledge graph, the learning-free and learning-free knowledge points having direct dependency relationship with the learned knowledge points are used as starting points. For example, starting from a system of unitary primary equations, a learning sequence of unitary primary equations, binary primary equations, and ternary primary equations may be generated based on the dependency relationship. Meanwhile, if other unlearned and unlearned knowledge points exist, such as a unified quadratic function (which has a dependency relationship with the unified first-order equation in terms of function-equation connection), another learning sequence, namely a unified first-order equation set and a unified second-order function, can be generated. Thus, a plurality of first learning sequences are generated.

And a fourth step of selecting one first learning sequence having the longest learning path from among the first learning sequences as a second learning sequence if a plurality of first learning sequences exist, and selecting a unique first learning sequence as a second learning sequence if the plurality of first learning sequences exist.

In the generated plurality of first learning sequences, their learned path lengths are compared. Assuming that the above-mentioned two learning sequences, the first learning sequence has 3 knowledge points and the second learning sequence has 2 knowledge points, then the first learning sequence (unitary system of once equations→binary system of once equations→ternary system of once equations) is selected as the second learning sequence because it has the longest learning path, covering review and consolidation of more relevant knowledge points.

In the related art, a learning sequence having a shorter learning path tends to be selected, and in this case, a longer learning sequence is selected. The learning sequence with longer path can provide motivation feedback for the learner in time to strengthen the learning interest of the learner, and the learning sequence with longer learning path can combine as many knowledge points as possible to establish learning logic with basic knowledge points as main line, and the knowledge points of the whole middle school mathematics are connected in series to establish the frame mathematical thinking of the learner.

Therefore, a lighter learning sequence of knowledge points can be constructed, and a learner can master knowledge more quickly. Fig. 5 is a schematic diagram of a second learning sequence in some embodiments of the application. As shown in fig. 5, 2 first learning sequences having 5 knowledge points are selected as the second learning sequences. Any one of the 2 learning sequences may be used as the second learning sequence.

And a fifth step of updating the knowledge points in the second learning sequence step by step in reverse order by taking the last knowledge point in the second learning sequence as a starting point to generate a target learning sequence, wherein the step of updating the knowledge points in the second learning sequence comprises the step of merging a plurality of front knowledge points into the front knowledge points of the rear knowledge points in the second sequence if the rear knowledge points in the second sequence have the plurality of front knowledge points in the second knowledge map.

FIG. 8 is a target learning sequence in some embodiments of the application. Taking the second learning sequence B- & gt ACD- & gt E- & gt F- & gt I as an example, in the second knowledge graph, the learning of the knowledge point I depends on GFH, so that in the updating process, the knowledge point G, the knowledge point F and the knowledge point H are combined to be changed into one knowledge point GFH, and the target learning sequence B- & gt ACD- & gt E- & gt GFH- & lt- & gt I is obtained after updating, so that the learning sequence has more knowledge points and is more beneficial to the systematic grasp of knowledge.

And gradually updating in reverse order by taking the last knowledge point (unitary one-time equation) in the second learning sequence as a starting point. In the second knowledge graph, knowledge points with direct dependency relationship with the unitary first-order equation and inequality related knowledge points (such as unitary first-order inequality) exist, and then the unitary first-order inequality is combined to serve as a previous knowledge point of the unitary first-order equation, and the updated learning sequence is changed into a unitary first-order inequality+unitary first-order equation, a binary first-order equation system and a ternary first-order equation system. Continuing the reverse order update, if the related knowledge of the set of inequalities (which is not considered before) is found to be related to the unitary one-time inequality, continuing to combine, and finally generating a target learning sequence which can help students learn related unknown knowledge systematically from the known knowledge and fully considers the dependency relationship among knowledge points.

The embodiment is performed on an online learning platform for mathematics in primary school. The platform has a complete mathematics knowledge database of middle school, and comprises the contents of detailed explanation, example questions, practice questions and the like of each knowledge point. Meanwhile, the platform can record the learning condition of each student on the knowledge points, and comprehensively judge the learning state of the knowledge points through various data such as training results, test achievements, learning time and the like of the students.

Fig. 6 is a schematic diagram of an online learning platform in some embodiments of the application. As shown in FIG. 6, the learning system comprises a learner, a server and a plurality of clients. The learner learns through the learning interface provided by the client, the client records the learning behavior of the learner, and the server is responsible for processing the data from the client and providing the processed data to the learner through the client.

Learners are subjects using the learning system, and they acquire knowledge and improve skills by accessing the system. The client presents an intuitive and easy-to-use learning interface for the learner. The interface is simple and clear in design, easy to operate and convenient for learners to quickly find out required learning resources, such as course catalogues, learning materials and the like. For example, the interface may present courses of different disciplines, different difficulty levels in the form of a classification menu that the learner may easily click into the course page of interest. In the process of learning by a learner through the learning interface, the client can record various learning behaviors of the learner in detail. These actions include, but are not limited to, learner access time to each course module, dwell time, learning order, answering situations (if there is a training or testing session), pausing and replaying of video play, etc. For example, when a learner is watching a certain mathematical course video, the client records the time point when he pauses the video at a certain knowledge point, and whether to replay the part of the content later, which may reflect the difficulty of the learner's understanding of the knowledge point.

The server is responsible for receiving learner learning behavior data from each client. It uses advanced data processing algorithms to analyze and process these data. For example, for answer data of the learner, the server may determine which knowledge points the learner has lower accuracy and which knowledge points are better mastered. For the learning time data, the service end can analyze the time trend of the learner in different courses so as to know the learning preference of the learner. The processed data is fed back to the learner again through the client. For example, after the server side analyzes that the learner has a weak link on a certain subitem of the english grammar, the client side pushes a specific learning suggestion, such as a related special exercise, supplementary data or other courses that recommend the knowledge point to be further taught. Meanwhile, the overall performance trend of the learner in the learning process, such as the completion condition of the learning progress, the change of the learning efficiency and the like, is displayed to the learner, so that the learner is helped to better know the learning condition of the learner.

Fig. 7 is a schematic diagram of a learning system in some embodiments of the application. As shown in fig. 7, the learning system includes a learning layer, a computing layer, a communication interface layer, a database, and other structures.

The application layer is the most direct layer of the learning system's interactions with the learner and the client. It is responsible for presenting various learning functions and services to learners, such as course management, learning planning, learning outcome presentation, etc. For example, a learner may set his own learning objectives and plans at the application layer, and the application layer may generate personalized learning path recommendations for the learner according to these settings, and track the execution of the plans during the learning process, so as to remind the learner of completing various learning tasks.

The computing layer takes on the main computing tasks in the system. The learning data is deeply mined and analyzed by using strong computing power. For example, the similarity between learners is calculated by a complex algorithm so as to recommend courses or learning methods selected by other learners having similar learning patterns and achieving good learning effects to the learners. Meanwhile, the calculation layer is also responsible for processing various model operations in the learning system, such as constructing a personalized learning model according to the historical learning data of the learner, and predicting the difficulty and learning effect possibly encountered by the learner in different learning scenes.

The communication interface layer ensures stable and efficient communication between the server and each client. The method can process a large amount of concurrent data transmission, and the communication interface layer can ensure the integrity and timeliness of the data no matter the learner uploads the operation data of the client to the server or downloads the feedback data processed by the server to the client. For example, during high concurrent learning peak hours, such as at night or on weekends, the communication interface layer can ensure that data interaction between each client and the server is not affected through an optimized communication protocol and data caching mechanism, and learning experience of learners is still smooth.

The database is a data storage center of the whole learning system. The learning system stores massive learning resource information, including video, documents, audio data and the like of various courses, and also stores personal information, learning history data, learning behavior records and the like of all learners. For example, when a learner needs to revisit a certain course which is learned before, the database can quickly and accurately call out relevant course data, learning progress of the learner in the course and other information, and support is provided for continuous learning of the learner. Moreover, the database can also be regularly backed up and optimized to ensure the safety of data and the efficient operation of the system.

The middle school mathematics knowledge graph covers all mathematics from first to third. Taking algebraic parts as examples, the algebraic parts include numbers and equations (rational numbers, irrational numbers, integral equations, partial equations, etc.), equations and inequalities (unitary first-order equations, binary first-order equation sets, unitary second-order equations, unitary first-order inequalities, etc.), functions (primary functions, secondary functions, inverse proportion functions, etc.). Geometric parts include triangle (nature of triangle, congruent triangle, similar triangle, etc.), quadrangle (parallelogram, rectangle, diamond, square, etc.), circle, etc. There are also knowledge points of the statistics and probability parts, such as collection and arrangement of data, calculation of probability, etc.

In algebra, the arithmetic rule of rational numbers is the basis of the integral arithmetic, because the coefficients in the integral arithmetic are rational numbers, and the proficiency of the addition, subtraction, multiplication and division of the rational numbers affects the integral arithmetic. For example, in the addition of the integer, it is necessary to add coefficients (rational numbers) of the same kind of terms.

For the equation part, the unitary first-order equation is the basis of the binary first-order equation set. The substitution elimination method of solving the binary primary equation set is to express one unknown number by using an equation containing another unknown number, and then substituting the equation into another equation to realize elimination, and the solution of the primary equation involved in the process.

In geometry, triangle interior angles and theorem are the basis for polygon interior angles and formula derivation. The polygon may be divided into a plurality of triangles, and the polygon interior angles and formulas may be deduced from the triangle interior angles and theorem.

In the functional part, the image of the primary function is a straight line, and the concepts of the slope and the intercept are closely related to the coefficient of the unitary primary equation. Solving the intersection point coordinates of the primary function and the coordinate axis is a command or, and the command or the coordinate is converted into the solution of a unitary primary equation.

The statistics and probability part, the collection and arrangement of data is the basis for calculating probability. Only if the data is accurately collected and collated, the frequency of occurrence of the event can be correctly calculated, thereby estimating the probability.

For each student, the platform determines the learning state of the knowledge points according to the following manner:

It is known that if the student has a correct rate of 90% or more in the practice problems associated with the knowledge point and the questions related to the knowledge point are all correct in the last chapter test, and the accumulated time for learning the knowledge point exceeds a certain threshold (set according to the difficulty level of the knowledge point, for example, 1 hour for a simple knowledge point and 3 hours for a complex knowledge point), it is determined that the student has mastered the knowledge point.

The student has not learned that the accuracy of the students in the practice problems related to the knowledge points is between 60% and 90%, or that the problems related to the knowledge points have partial errors in the chapter test, and the learning time reaches a certain degree (such as 0.5 hour for a simple knowledge point and 2 hours for a complex knowledge point).

If the student never touches the learning material related to the knowledge point or the learning time is extremely short (below the time threshold set above), it is determined that the student is not learning and not mastering.

The first step performs an example. Taking a student learner as an example, the platform obtains information from its knowledge graph. In the algebraic section, the learner has learned the state of the unitary first-order equation, has learned the state of the unitary second-order equation (he can solve some simple unitary second-order equations but often makes mistakes in solving the problem by Wei Da's theorem), and has learned the state of the higher-order equation (e.g., the third-order equation). In the geometric section, the learner has learned about the nature of the triangle, has learned about the judgment theorem of the similar triangle (sometimes confusing different judgment methods), and has not learned about the relevant knowledge of the circle.

Meanwhile, the platform definitely shows the dependency relationship among knowledge points. In algebra, the solving method (a method, a formula method and the like) of the unitary quadratic equation has a dependency relationship with the operations of the shifting term, the formula and the like of the unitary quadratic equation, and in geometry, the judgment of the similar triangle has a dependency relationship with the internal angle and theorem of the triangle, the proportional relationship of the edges and the like.

The second step performs an example. Assume that the learner has a unitary one-time equation and a full-form multiplication at knowledge points that the algebraic part has mastered. The platform starts with the unitary one-time equation, finds that there is a direct dependency relationship with the multiplication of the integer (the multiplication of the integer may be involved in the denominator step of solving the unitary one-time equation), and merges them. Meanwhile, the isolated knowledge points which are irrelevant to the knowledge points which are mastered and not mastered at present, such as a certain ancient mathematical notation (the correlation between the current middle school mathematical learning and the subsequent learning is extremely small) are deleted, and a second knowledge map is generated. In this second knowledge graph, the dependency relationship between the knowledge points (such as solving by factorization of a unitary quadratic equation, which has a certain correlation with the integral multiplication) which are not mastered is preserved.

The third step performs an example. And selecting an unlearned knowledge point which has a direct dependency relationship with the mastered knowledge point from the newly generated second knowledge map as a starting point. For the learner, in the algebraic part, a first learning sequence is generated by taking the factorization solution of the unitary quadratic equation as a starting point, namely, the unitary first-order equation (consolidation), the integral multiplication (review) and the factorization solution of the unitary quadratic equation. If other unlearned knowledge points exist, such as a partial equation (the denominator removing step in the solving process is related to integral multiplication), another learning sequence can be generated, namely the partial equation, the integral multiplication and the unitary one-time equation. This generates a plurality of first learning sequences for the learner in the algebraic part.

The fourth step performs an example. The learned path lengths of these first learned sequences are compared. Assuming the two learning sequences mentioned above, the first learning sequence has 3 knowledge points and the second learning sequence has 3 knowledge points (here, just examples, may be different in practice). Further comparing the depth of association and coverage between knowledge points, if the first learning sequence is more comprehensive in review and consolidation of relevant knowledge (e.g., involves more types of integer multiplication review and the application of one-time equations in factorization), then the first learning sequence is selected as the second learning sequence.

The fifth step performs an example. And gradually updating in reverse order by taking the last knowledge point (unitary one-time equation) in the second learning sequence as a starting point. In the second knowledge graph, the application knowledge points (such as travel problems, engineering problems and the like) of the unified primary equation and the unified primary equation are found to have direct dependency relationship with the unified primary equation, the application knowledge points of the unified primary equation are combined to serve as the previous knowledge points of the unified primary equation, and the updated learning sequence is changed into the factorization solution of the unified secondary equation, the integral multiplication, the application of the unified primary equation and the unified primary equation. And continuing to update in the reverse order, if the quantitative relation analysis knowledge points in the actual problems are found to be related to the application of the unitary primary equation, continuing to combine, finally generating a target learning sequence suitable for a learner, helping the learner to learn the factor decomposition method of the Xi Yiyuan secondary equation more efficiently from the mastered knowledge to solve the non-mastered knowledge points, and simultaneously consolidating related basic knowledge and related knowledge.

For students who are about to learn a new chapter, such as students who are about to learn a new three-round chapter. The platform generates a pre-learned learning sequence by the method according to the previous mastering conditions of the geometric knowledge (such as the mastering states of related knowledge such as triangles, quadrilaterals and the like) of students. And (3) starting from the mastered geometric basic knowledge, finding out the dependency relationship with the round related knowledge points, generating a learning sequence, and enabling students to know the relationship between the round and the previous knowledge in a targeted manner in the pre-learning process, so that new contents can be better understood.

In the examination review stage at the end of the period, students with poor knowledge mastery conditions of the whole algebra are presented. The platform generates a learning sequence for review according to the learning state of students at various algebraic knowledge points (from numbers and equations to inequality, functions and the like). For example, starting from the mastered unitary one-time equation, the review sequence of the whole algebraic part is carded out through the knowledge graph and the dependency relationship, and the knowledge points can be better helped to understand and consolidate other knowledge points, so that the review efficiency is improved.

For students with learning redundancy, it is desirable to develop mathematical knowledge. The platform can generate a learning sequence according to the dependency relationship between the expansion part of the middle school mathematic knowledge graph (such as the related knowledge points of the competition mathematics) and the normal teaching knowledge points. For example, starting from the mastered function knowledge, a learning sequence is generated for students, and the students are guided to learn advanced knowledge of the function, such as iteration of the function, motionless points and other competition related contents, so that the students are helped to develop knowledge gradually.

By comparing the time it takes for the students to complete the same learning task (e.g., grasp a new knowledge point or review a chapter) before and after using the method. If the time spent by students is obviously reduced (for example, by more than 20 percent) after the method is used, the learning efficiency is obviously improved.

By analyzing the student's performance in knowledge point related practice problems and tests. If the accuracy of the test related to the knowledge points is obviously improved (for example, the accuracy is improved by more than 15 percent) after the students learn the learning sequence generated by using the method, the mastering degree of the knowledge points is improved.

The matching degree of the learning path of the student in the learning process and the knowledge point dependency relationship in the knowledge graph is analyzed. If the learning path of the student is highly consistent with the dependency relationship (for example, more than 80% of knowledge point learning sequences are consistent with the dependency relationship), the learning path is reasonable.

After 100 students are subjected to experiments for one learning period, the learning efficiency of the students using the method is obviously improved. In the new knowledge point learning task, the average learning time is reduced by about 25%. The test performance is improved by about 20% on average at the knowledge point mastery level. Meanwhile, analysis of the learning path of the students shows that about 85% of the learning path of the students is well matched with the dependency relationship in the knowledge graph, and the learning sequence generation method has good application effect in mathematics learning of middle school.

The learning sequence generation method based on the learning relation has important significance in middle school mathematics learning. Through scientifically analyzing the learning state and the dependency relationship of the knowledge points, a personalized learning sequence is generated for students, and the learning efficiency and the grasping degree of the knowledge points can be effectively improved. The method has good application effects in learning scenes such as pre-learning, review and knowledge expansion, and provides an innovative auxiliary learning means for mathematics education in middle school. In future development, the knowledge graph construction and learning state judgment method can be further optimized so as to better adapt to learning requirements of different students. Meanwhile, the method can be expanded to other disciplinary fields, and more powerful support is provided for the comprehensive study of students.

In some embodiments, the fourth step of selecting one of the one or more first learning sequences having the longest learning path as the second learning sequence includes selecting, as the second learning sequence, the first learning sequence having one of the knowledge points having the most direct dependency relationship with the first learning sequence if there are a plurality of first learning sequences having the longest learning path. Therefore, a learning sequence of knowledge points with wider association can be constructed, and the learner can learn more systematically.

In some embodiments, the fourth step of selecting one of the one or more first learning sequences having the longest learning path as the second learning sequence includes selecting, as the second learning sequence, the first learning sequence having one of the knowledge points having the least direct dependency relationship with the first learning sequence if there are a plurality of first learning sequences having the longest learning path. Therefore, a lighter learning sequence of knowledge points can be constructed, and a learner can master knowledge more quickly.

The scheme is a knowledge graph updating mechanism. As students learn, learning states and dependencies in the knowledge graph may change. For example, updates to the content of a teaching material may result in adjustment of the dependency between knowledge points, or a student may change its learning state after relearning a certain knowledge point. Thus, updating the first knowledge-graph on a regular basis (e.g., weekly or monthly) is critical to ensuring timeliness and accuracy of the learning sequence.

When the learning state is updated, the system re-analyzes the data of the students in the recent learning activities, including new exercise results, test achievements, learning time changes and the like. For the update of the dependency, the platform will refer to the educational specialist's advice, new teaching outline and the latest teaching material content. For example, if the new teaching material adjusts the teaching sequence of the function or increases the contact content of the function and other knowledge points, the system will modify the dependency relationship in the knowledge graph accordingly, so as to ensure that the learning sequence generated later meets the latest teaching requirement.

The platform provides a visual display interface of the learning sequence for the students. The learning sequence is presented in a graphical manner, each knowledge point is represented by a node, and the dependency between knowledge points is represented by an arrow. For example, when a learning sequence of the application of the root equation of the unitary quadratic equation is displayed, nodes are the application of the root equation of the unitary quadratic equation, integral multiplication, practical application of the unitary primary equation and the unitary primary equation respectively, and the arrow direction clearly displays the association between the learned sequence and knowledge points from back to front.

In addition to learning sequences, the entire middle school mathematical knowledge graph can also be visually displayed. Students can view the location of individual knowledge points in the knowledge hierarchy and their broad association with other knowledge points. This helps students understand the mathematical knowledge structure from a macroscopic perspective, enhancing the sense of identity to the learning sequence and the planning of the overall learning. For example, when looking at algebraic knowledge graphs, students can see knowledge venues from rational numbers to various equations and functions, and understand the roles of the currently learned knowledge points in the whole algebraic system.

The platform provides multiple feedback channels for students, such as on-line questionnaires, commentary areas, special feedback buttons, and the like. Students can feed back contents such as satisfaction degree of learning sequences, difficulty in learning process, advice of learning sequence to a certain knowledge point and the like. For example, when a student learns knowledge of a circle in geometry according to a learning sequence, the student may find that the knowledge point sequence of a certain step is not well in accordance with his understanding habit, and may inform the platform through feedback.

According to student feedback, the system adjusts the generation strategy of the learning sequence. If the sequence of feeding back a certain knowledge point in a certain learning sequence by a plurality of students is unreasonable, the system can re-analyze the dependency relationship of the knowledge point in the knowledge graph and the learning data of the students, and consider whether the learning sequence needs to be adjusted. Meanwhile, if the student proposes a new learning target (such as learning a certain competition related knowledge point in advance), the system can try to generate a new learning sequence for the student or adjust an existing learning sequence on the premise of meeting the current learning progress and knowledge dependency relationship.

The platform associates each knowledge point in the learning sequence with a corresponding learning resource. The knowledge point is applied to the root equation of the unitary quadratic equation, and the associated resources comprise video courses for explaining the derivation process of the equation, different types of practice problems (basic problems, improvement problems and expansion problems), related simulation test problems, practical application case analysis and the like. Therefore, students can conveniently acquire the resources matched with the current learning knowledge points in the learning process, and the learning effect is improved.

According to the learning state and learning progress of the students, the system can also recommend personalized learning resources. If students show a learned and unoccupied state on the application knowledge points of the root equation of the unitary quadratic equation, the system may recommend more special exercises and detailed explanation videos, and help students to strengthen understanding and mastering the knowledge points.

The system records in detail the learning progress and performance of the student in the learning process according to the learning sequence. For each knowledge point, information such as the time when the student starts to learn, the time when the student finishes learning, the number of pauses in the learning process, the accuracy of the exercise and the like is recorded. For example, when learning the root formula of the unitary quadratic equation and applying knowledge points, the time span from the first opening of the relevant learning resources to the completion of all recommended practice problems and the answering situation in the practice problems are recorded for students.

If the student has learned knowledge points in the learning process, the system regenerates the target learning sequence. For example, after the application of the root equation of the learning unitary quadratic equation, the student performs poorly in subsequent tests, indicating that the knowledge point is not mastered. The system re-analyzes the knowledge graph, considers other knowledge points related to the application of the root formula of the unitary quadratic equation, such as re-reviewing the basic concepts and the method of the unitary quadratic equation, and generates a new learning sequence to help students to re-consolidate and master the knowledge points so as to better promote subsequent learning.

Claims

1. A method for generating a learning sequence based on a learning relationship, characterized in that it comprises the following steps:

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. According to the learning relationship-based learning sequence generation method of claim 1, it is characterized in that the way of obtaining the learning status of the knowledge point includes: automatically recording and analyzing the learner's learning behavior data or the learner's input through the learning system.

3. According to the learning relationship-based learning sequence generation method of claim 1, it is characterized in that the basis for determining the learning status includes the learner's test scores on relevant knowledge points.

4. According to the learning relationship-based learning sequence generation method described in claim 1, it is characterized in that when generating the second knowledge graph, the merged and mastered knowledge points are marked to distinguish them from the knowledge points that have not been merged, the merge mark can be removed, and the merged and mastered knowledge points after the mark is removed can be restored.

5. The learning relationship-based learning sequence generation method according to claim 1 is 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 the first learning sequence with the most directly dependent knowledge points in the second knowledge graph is selected as the second learning sequence.

6. The learning relationship-based learning sequence generation method according to claim 1 is 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 the first learning sequence with the least direct dependency knowledge points in the second knowledge graph is selected as the second learning sequence.

7. According to the learning relationship-based learning sequence generation method of claim 1, it is characterized in that the learning status and dependency relationships in the first knowledge graph are regularly updated 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 a visual display of the learning sequence is provided.

9. The learning sequence generation method based on learning relationship according to claim 1 is characterized in that 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.

10. The learning relationship-based learning sequence generation method according to claim 1 is 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 if there are knowledge points that have been learned but not mastered, the target learning sequence is regenerated.