Personalized exercise resource recommendation method and system based on solution strategy

Abstract

The present invention provides a personalized exercise resource recommendation method and system based on solution strategy, wherein the method first obtains a set of knowledge blind spots of learners, then constructs a strategy-level knowledge graph, closely combines learning strategies with knowledge concepts, and generates a multi-level, strategy-oriented knowledge network. Then, knowledge concept learning paths based on the strategy-level knowledge graph are generated to generate a personalized learning path for students that takes into account the logical order and difficulty of knowledge, so as to assist students in learning and mastering relevant knowledge in the shortest possible time and with the most efficient learning path. Finally, exercise resource recommendation based on solution strategy is performed to recommend exercise resources that match the current learning path to students. Through a two-way mapping relationship, the final recommended exercise resources not only cover the knowledge concepts that students need to master, but also incorporate exercise solution strategies, thereby greatly improving the recommendation effect of personalized exercise resources.

Description

Technical Field

[0001] The present invention relates to the field of personalized recommendation technology, and in particular to a personalized exercise resource recommendation method and system based on solution strategy. Background Art

[0002] In today's information age, the number and diversity of educational resources are already very rich. Students and users are faced with a variety of choices in learning and entertainment. However, massive data brings a huge challenge: how to find the most suitable resources among the massive educational resources. Personalized recommendation systems provide students with the most efficient learning resource recommendations.

[0003] The core idea of ​​the personalized educational resource recommendation system is to recommend the most suitable courses, textbooks, videos and other teaching contents to students by analyzing their behaviors and preferences, such as learning history, interests and needs.

[0004] The personalized educational resource recommendation methods in the prior art generally include the following:

[0005] 1) Content-based recommendation: Content-based recommendation algorithms recommend the most similar resources to students by analyzing the characteristics of educational resources, such as titles, descriptions, tags, etc. The core of the algorithm is to measure the similarity between items by distance.

[0006] 2) Recommendation based on collaborative filtering: Collaborative filtering is a recommendation algorithm based on student behavior. It analyzes the similarities between students and recommends resources that similar students like. Collaborative filtering can be divided into student-based collaborative filtering and educational resource-based collaborative filtering.

[0007] 3) Hybrid recommendation: Hybrid recommendation is a method that combines multiple recommendation algorithms to make full use of different information sources such as content and collaborative filtering to improve the quality of recommendations.

[0008] However, existing personalized exercise resource recommendation algorithms in the field of higher mathematics mainly focus on students' learning status and cognitive status at the knowledge concept level, ignoring the classic problem-solving rules and theorems in mathematical problems, making these methods ineffective in exercise recommendation. Summary of the invention

[0009] The present invention provides a method and system for recommending personalized exercise resources based on a solution strategy, which are used to solve or at least partially solve the technical problem of poor recommendation effect existing in the prior art.

[0010] In order to solve the above technical problems, the technical solution adopted by the present invention specifically includes:

[0011] The first aspect discloses a personalized exercise resource recommendation method based on a solution strategy, comprising:

[0012] Analyze learners' feedback data and learning behaviors to obtain learners' knowledge blind spots.

[0013] Extract metadata to construct a strategy-level knowledge graph, where metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer takes the solution strategy as an entity, and the degree of association between solution strategies as the relationship between entities. The problem resource layer takes each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer takes each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer.

[0014] According to the knowledge blind spot set or the selection of the target knowledge concept, the target knowledge concept is obtained. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced using topological sorting to generate a knowledge concept learning path that takes into account the logical order and difficulty of knowledge.

[0015] Based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer, a sequence of exercise resources to be recommended is generated.

[0016] In one embodiment, extracting metadata to construct a policy-level knowledge graph includes:

[0017] Collect math problem resources, extract and annotate the knowledge concepts and solution strategies in the math problem resources, calculate the degree of fit between the two strategies based on the probability of a solution strategy appearing alone in a math problem resource and the probability of two different solution strategies appearing together in the same math problem resource, and obtain a fit matrix, where the elements in the fit matrix are used to measure the degree of association between the two solution strategies;

[0018] Based on the TF-IDF algorithm (term frequency–inverse document frequency), the knowledge concepts in the math problem resources are weighted to determine the importance of the knowledge concepts;

[0019] The knowledge concept layer is constructed according to the extracted and labeled knowledge concepts and the importance of the knowledge concepts. The solution strategy layer is constructed according to the labeled solution strategies and the coordination matrix. The exercise resource layer is constructed according to the exercise resources and the learning order of the exercise resources.

[0020] In one embodiment, the marked solution strategies include: function thinking, limit thinking, reduction thinking, analogy thinking, number-shape combination thinking, mathematical modeling thinking, overall and local thinking, classification discussion thinking and unknown type thinking.

[0021] In one implementation, the learner's knowledge blind spot set includes knowledge concepts that the learner has not mastered, and according to the knowledge blind spot set or the selection of the target knowledge concept, obtaining the target knowledge concept includes:

[0022] If the learner has selected the knowledge concept to be learned, the selected knowledge concept is used as the target knowledge concept; otherwise, the last knowledge concept in the knowledge blind spot set is used as the target knowledge concept.

[0023] In one embodiment, based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer, a sequence of exercise resources to be recommended is generated, including:

[0024] In the exercise resource layer of the strategy-level knowledge graph, all exercise resources that have a mapping relationship with the knowledge concepts included in the knowledge concept learning path are searched;

[0025] Based on the mapping relationship between the exercise resource layer and the solution strategy layer, the queried exercise resource sequence is mapped to the solution strategy layer, and the exercise resources corresponding to the solution strategy with the highest degree of coordination with the target solution strategy are screened out;

[0026] According to the learning order of knowledge concepts, multiple corresponding exercise resource sequences are sorted, and finally a sequence of exercise resources to be recommended is generated.

[0027] In one implementation, based on the mapping relationship between the exercise resource layer and the solution strategy layer, the queried exercise resource sequence is mapped to the solution strategy layer, and the exercise resources corresponding to the solution strategy with the highest degree of compatibility with the target solution strategy selected by the user are screened out, including:

[0028] Personalized solution strategy marking for exercise resources, including: obtaining all solution strategies of exercise resources that have a mapping relationship with the knowledge concepts in the knowledge concept learning path, judging whether all solution strategies contain the target solution strategy that the user wants to learn, and if so, using Mark this exercise resource, where Represents exercise resources, represents the target solution strategy, express Otherwise, compare the correlation between all solution strategies and the target solution strategy, and find the solution strategy with the highest correlation with the target solution strategy according to the matching value. ,according to The order of the solution strategy in the fitness matrix To mark this exercise resource , Represents a solution strategy and The compatibility value of

[0029] For all marked exercise resources, mark them with The exercise resources are retained, and other exercise resources are Sort by size and keep The exercise resource with the largest value is selected, and the rest are deleted. The exercise resources retained are the exercise resources corresponding to the solution strategy with the highest degree of fit with the target solution strategy.

[0030] Based on the same inventive concept, the second aspect of the present invention discloses a personalized exercise resource recommendation system based on a solution strategy, comprising:

[0031] The cognitive status diagnosis module is used to analyze the learner's feedback data and learning behavior to obtain the learner's knowledge blind spot set;

[0032] The knowledge graph construction module is used to extract metadata to construct a strategy-level knowledge graph, where the metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer uses solution strategies as entities, and the degree of association between solution strategies as the relationship between entities. The problem resource layer uses each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer uses each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer.

[0033] The knowledge concept learning path generation module is used to obtain the target knowledge concept according to the knowledge blind spot set or the selection of the target knowledge concept. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced by topological sorting to generate a knowledge concept learning path that takes into account the logical order and difficulty of knowledge.

[0034] The exercise resource recommendation module is used to generate a sequence of exercise resources to be recommended based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer.

[0035] Based on the same inventive concept, the third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the personalized exercise resource recommendation method based on solution strategies described in the first aspect.

[0036] Based on the same inventive concept, the fourth aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the personalized exercise resource recommendation method based on the solution strategy described in the first aspect is implemented.

[0037] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows:

[0038] The present invention proposes a personalized exercise resource recommendation method based on solution strategy. By deeply analyzing students' feedback data and learning behavior, the student's knowledge blind spot set is accurately identified, providing a clear recommendation basis for subsequent exercise resource recommendation. A strategy-level knowledge graph is constructed. Compared with the single-level entity association of the traditional knowledge graph, the strategy-level knowledge graph closely combines learning strategies with knowledge concepts to generate a multi-level, strategy-oriented knowledge network. The strategy-level knowledge graph not only contains the multi-level structure and entity association of knowledge, but also merges the exercise resources and solution strategies that have an upper-level mapping relationship with the lower-level knowledge concept layer. The knowledge concept learning path generation based on the strategy-level knowledge graph is performed: after obtaining the student's knowledge blind spot set and target knowledge concept, a personalized learning path that takes into account the logical order and difficulty of knowledge is generated for the student according to the strategy-level knowledge graph, which assists students to learn and master relevant knowledge in the shortest possible time with the most efficient learning path. Finally, exercise resources are recommended based on solution strategies: after the knowledge concept learning path is generated, according to the upper and lower hierarchical mapping relationship between knowledge concepts and exercise resources in the strategy-level knowledge graph, the knowledge concept layer is forward mapped to the exercise resource layer, and then forward mapped to the solution strategy layer, and then reversely mapped from the solution strategy layer to the exercise resource layer. As the final recommendation result, exercise resources that match the current learning path are recommended to students. Through the above two-way mapping relationship, the final recommended exercise resources not only cover the knowledge concepts that students need to master, but also incorporate exercise solution strategies, which can achieve the effect of improving exercise recommendations. In practical applications, it can help students consolidate their knowledge and improve their problem-solving ability in the process of solving logical math problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 A flowchart of a method for recommending personalized exercise resources based on a solution strategy provided by an embodiment of the present invention;

[0041] Figure 2 A schematic diagram of a strategy-level knowledge graph constructed for an embodiment of the present invention;

[0042] Figure 3 A schematic diagram of solving a strategy coordination matrix in an embodiment of the present invention;

[0043] Figure 4 A schematic diagram of knowledge concept path generation in an embodiment of the present invention;

[0044] Figure 5 A schematic diagram of selecting exercise resources in an embodiment of the present invention;

[0045] Figure 6 A comparison diagram of the pre-test stage and the post-test stage of students in an embodiment of the present invention;

[0046] Figure 7 This is a schematic diagram of the satisfaction survey results of the recommended method in the embodiment of the present invention;

[0047] Figure 8 Schematic diagram of satisfaction survey results of the recommendation system in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The present invention proposes a personalized exercise resource recommendation method based on a solution strategy, which mainly includes the following steps:

[0049] Step 1: Use the neurocognitive diagnostic model to analyze the learner's feedback data and learning behavior to obtain the learner's knowledge blind spot set;

[0050] Step 2: Extract policy-level knowledge graph metadata and construct a policy-level knowledge graph; specifically, it includes:

[0051] 2.1: Collect math problem resources: Collect math problem pictures in png format (Portable Network Graphics, a bitmap file storage format).

[0052] 2.2: Annotate exercise resources: Experts will annotate the exercise resources, including the knowledge concepts involved in each exercise and the solution strategies used.

[0053] 2.3: Determine the importance of knowledge concepts: Use the TF-IDF algorithm to weight the knowledge concepts within the exercise resources to determine their importance.

[0054] 2.4: Limit the number of knowledge concepts: Limit the number of knowledge concepts for each resource according to the importance of the knowledge concepts and save them as a data set in CSV format.

[0055] 2.5: Calculate the degree of coordination of solution strategies: Find the implicit relationship between solution strategies, calculate the PMI value based on the co-occurrence probability and single occurrence probability of solution strategies, define it as the degree of coordination, and construct the solution strategy coordination matrix based on it.

[0056] Step 3: Generate a learning path based on the policy-level knowledge graph, including:

[0057] 3.1: Determine the target knowledge concept: If the student has clearly selected the target knowledge concept, it will be set as the end point of the learning path. If the student has not clearly selected the target knowledge, the system will select the last one among the unmastered knowledge as the target knowledge concept based on the results of the cognitive diagnosis module.

[0058] 3.2: Exclude already mastered knowledge: Consider the knowledge concepts that students have already mastered. For example, the knowledge concept sets outside the knowledge blind spot set of the neurocognitive diagnosis model are all knowledge that students have already mastered. This mastered knowledge will not be displayed in the learning path to avoid redundant learning content.

[0059] 3.3: Dynamic path generation: In the knowledge concept hierarchy of the knowledge graph, the student's target knowledge concept is taken as the end point. Then, using topological sorting technology, the dependency relationship of the target knowledge in the knowledge concept layer in the hierarchical knowledge graph is reversely traced, thereby generating a dynamic learning path from simple to difficult, from the knowledge concept of the current cognitive state to the target knowledge concept step by step.

[0060] Step 4: Personalized exercise resource recommendations based on solution strategies, including:

[0061] 4.1: Query the sequence of exercise resources corresponding to knowledge concepts: Query all exercise resources in the exercise resource layer of the knowledge graph that contain the mapping of each knowledge concept on the learning path solved based on the strategy-level knowledge graph.

[0062] 4.2: Map and screen the solution strategies for the exercise resource sequence: Map the exercise resource sequence of each knowledge concept on the learning path to the solution strategy layer, and screen out the exercise resources corresponding to the solution strategy that best matches the target solution strategy.

[0063] 4.3: Generate exercise resource sequence: Sort the corresponding multiple exercise resource sequences according to the order of knowledge concepts, and finally generate the exercise resource sequence to be recommended.

[0064] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] Embodiment 1

[0066] The present invention discloses a personalized exercise resource recommendation method based on solution strategy, see Figure 1 , the method comprising:

[0067] S1: Analyze learners’ feedback data and learning behaviors to obtain learners’ knowledge blind spot set;

[0068] S2: Extract metadata to build a strategy-level knowledge graph, where metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer uses solution strategies as entities, and the degree of association between solution strategies as the relationship between entities. The problem resource layer uses each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer uses each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer.

[0069] S3: According to the knowledge blind spot set or the selection of the target knowledge concept, the target knowledge concept is obtained. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced by topological sorting to generate a knowledge concept learning path that considers the logical order and difficulty of knowledge.

[0070] S4: Generate a sequence of exercise resources to be recommended based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer.

[0071] Specifically, S1 is the identification of knowledge state. In the specific implementation process, the cognitive diagnosis model based on the hypergraph can be used to model the cognitive state of students to obtain the current knowledge mastery of students. The cognitive diagnosis model provides a knowledge state prediction method based on the modified Q matrix and the hypergraph attention network. The existing modified Q matrix based on the knowledge concept prerequisite dependency graph is used to diagnose students' knowledge concepts, overcoming the problem that the expert Q matrix in the traditional cognitive diagnosis model is prone to errors and the manual consumption of annotation is too large. Secondly, the modified Q matrix ignores the association between exercises, which makes the difficulty discrimination of knowledge concepts insufficient, resulting in low accuracy of cognitive diagnosis results. In order to improve the difficulty discrimination of knowledge concepts, an exercise association measurement model based on the hypergraph attention mechanism is proposed to obtain more accurate exercise similarity. The difficulty discrimination of knowledge concepts is improved by improving the similarity of exercises. Finally, in the diagnosis stage, by introducing Transformer to the item response theory for information aggregation and updating, the optimal knowledge concept proficiency is predicted, and finally the student's knowledge state is obtained, and the knowledge blind spot set is obtained.

[0072] S2 is the construction of the strategy-level knowledge graph: Compared with the single-level entity association of the traditional knowledge graph, the strategy-level knowledge graph closely combines learning strategies with knowledge concepts to generate a multi-level, strategy-oriented knowledge network. The strategy-level knowledge graph not only contains the multi-level structure and entity association of knowledge, but also merges the exercise resources and solution strategies that have an upper-level mapping relationship with the lower-level knowledge concept layer.

[0073] S3 generates learning paths based on the strategy-level knowledge graph. According to the strategy-level knowledge graph, it generates a personalized learning path for students that takes into account the logical order and difficulty level of knowledge, helping students to learn and master relevant knowledge in the shortest possible time and with the most efficient learning path.

[0074] S4 is the recommendation of exercise resources based on solution strategies: after generating the knowledge concept learning path, according to the upper and lower hierarchical mapping relationship between knowledge concepts and exercise resources in the strategy-level knowledge graph, the knowledge concept layer is forward mapped to the exercise resource layer, and then forward mapped to the solution strategy layer, and further reversely mapped from the solution strategy layer to the exercise resource layer. As the final recommendation result, exercise resources matching the current learning path are recommended to students.

[0075] The following is an explanation of the specific implementation steps:

[0076] 1. The construction of the knowledge graph includes knowledge concept extraction from mathematical resources, TF-IDF algorithm weighting, and relationship construction

[0077] 1.1 Knowledge concept extraction from mathematical resources

[0078] 1.1.1 Data Source and Labeling

[0079] The advanced mathematics problem resources used in this embodiment mainly include three categories: Tongji University's seventh edition of "Advanced Mathematics", the real questions of the mathematics subjects of the national postgraduate entrance examination in previous years (including Mathematics I, Mathematics II and Mathematics III), and postgraduate entrance examination guidance books. These resources almost cover all the knowledge concepts and applications of advanced mathematics. Solving the exercises in these resources requires the comprehensive use of multiple knowledge concepts and solution strategies. Therefore, the present invention adopts a method of labeling the problem-solving steps with knowledge concepts and solution strategies to extract relevant knowledge concepts and solution strategies.

[0080] The undergraduate textbook "Advanced Mathematics" is compiled by the Department of Mathematics of Tongji University and is also one of the designated textbooks for postgraduate entrance examinations in mathematics. The textbook clearly divides chapters and knowledge concepts, with a total of 82 knowledge concepts. This invention names them in the format of "chapter number. knowledge concept number. knowledge concept name", plus 9 basic knowledge concepts for advanced mathematics, a total of 91 knowledge concepts, which are reasonably divided to ensure the accurate positioning and completeness of knowledge concepts.

[0081] 1.1.2 Knowledge Concept Annotation Process

[0082] In order to solve the problem of inconvenience in identifying and dividing the problem-solving steps caused by saving higher-level mathematics exercise resources in the form of images, this embodiment adopts optical character recognition (OCR) technology. Specifically, the present invention uses SimpleTex (a formula recognition software) recognition software to convert the mathematical content in the image into LaTeX (a markup language) markup language format, thereby effectively extracting mathematical expressions. After successful conversion, the extracted mathematical expressions are further sorted and organized into a clear sequence of problem-solving steps. These sequences are then annotated, and finally a knowledge concept sequence of higher-level mathematics exercise resources is generated, which greatly improves the recognizability and parsability of the exercise resources.

[0083] Use the screenshot tool that comes with the computer system to capture the questions and solution steps of the exercise resources respectively, and save them in png format. The questions are divided into two categories: teaching supplementary question resources and postgraduate entrance examination question resources. The specific naming rules are: 1) Teaching supplementary category: publication year-book type-ISBN-chapter number-exercise type-question number-resource type.png. For example, 2022-01-9787109455491-01-01-01-q.png, this label example can be explained as follows: the resource in the picture comes from the 2022 postgraduate entrance examination Mathematics I teaching and tutoring book (01 represents Mathematics I, 02 represents Mathematics II, and 03 represents Mathematics III), the ISBN number (International Standard Book Number ‌ International Standard Book Number) of the teaching aid is "9787109455491", the exercise resource is the multiple-choice questions in the first chapter of this book (01 represents multiple-choice questions, 02 represents fill-in-the-blank questions, and 03 represents answer questions), the exercise resource is the first question in this chapter, and the exercise resource is the question part of the question (q represents the question part, and a represents the solution step part). 2) Real exam type: year-exam type-exercise type-question number-resource type.png. For example, 2021-02-01-05-a.png, this label example can be explained as follows. This screenshot shows the solution steps for the fifth multiple-choice question in the Mathematics II test paper of the 2021 National Postgraduate Entrance Examination.

[0084] The specific process is as follows:

[0085] In the process of optimizing the processing of advanced mathematics problem resources, we first focus on the mathematical resource images in the problem-solving steps. These images are converted through the OCR (optical character recognition) interface of the SimpleTex tool, converting them from the original image format to the LaTeX markup language format. This allows complex mathematical formulas to be recognized as symbolic languages ​​that can be understood by computers.

[0086] Filter the content of the exercise resources and keep only the set of expressions. In LaTeX format text, formulas are wrapped with $. Using regular expressions to filter the parts wrapped with $ can match all mathematical expressions.

[0087] In the exercise resources, expressions may contain multiple operators of different types. These operators are not only assignment operators (such as "="), but also comparison operators (such as ">", "<", "≠"), logical operators (such as "AND", "OR", "NOT" or the symbol "~"), and other mathematical operators. When a mathematical expression uses a mixture of these operators, it may involve multiple knowledge concepts at the same time, which increases the difficulty of understanding and annotation. In order to perform more detailed manual annotation, an effective strategy is to split and regroup the formula according to the type of these operators.

[0088] For example, formula (1)

[0089] (1)

[0090] Set up Exercise Resources , the resource expression There are assignment operators, where It is a mathematical resource The total number of expressions split out, This is the first SplicExpression() is a function used to connect two expressions. The two adjacent expressions in the expression are concatenated one by one using this function, and finally a set of expressions is obtained. .

[0091] After each exercise resource is annotated, a JSON file is generated. This file records in detail the number of the annotated image, the expression content, and the corresponding knowledge concept label. In this way, the annotated data can be systematically stored and managed for subsequent query, analysis, and utilization.

[0092] In order to build a complete data set for subsequent cognitive diagnosis and personalized exercise resource recommendation, all the knowledge concept names and expressions of the exercise resources are integrated into a CSV (Comma-Separated Values) file. This CSV file is in a table format, where each line represents a math resource record. Specifically, each line will contain three main fields: the unique number of the math exercise resource, the math expression contained in the resource, and the corresponding knowledge concept.

[0093] The final generated mathematics exercise resource knowledge concept dataset contains a total of 1578 exercise resources, of which there are 11489 expressions screened out in the problem-solving steps and the number of knowledge concept types is 91. 13 categories can be obtained by chapter, among which the additional added advanced mathematics prerequisite knowledge concepts are made into a separate chapter category. Since many exercise resources contain knowledge concepts that are difficult to judge, some labels may contain noise. After removing the knowledge concepts that do not contain mathematical semantics and noise labels, there are finally 1245 exercise resources that can be used, with a total of 82 categories of knowledge concepts and a total of 5021 knowledge concepts.

[0094] 1.1.3 Solution Strategy Labeling Process

[0095] Since the solution strategy is a mathematical definition with higher semantics, it is relatively abstract and difficult to define clearly. First, the commonly used solution strategies are classified and listed, and the following categories of solution strategies are summarized:

[0096] Functional thinking: Functional thinking is a way of thinking that solves problems by studying the dependencies between variables. It emphasizes the changing rules and corresponding relationships of variables and is one of the core methods for understanding and solving mathematical problems.

[0097] Limit thinking: Limit thinking involves studying the behavior of a variable as it approaches a certain value. It is the foundation of calculus and describes concepts such as continuity, derivatives, and integrals.

[0098] Reduction thinking: Reduction thinking is a way of thinking that transforms complex problems into problems that have been solved or are relatively easy to solve. This thinking is often used in mathematical proofs and problem solving, and achieves the goal through simplification or induction.

[0099] Analogy thinking: Analogy thinking is a way of thinking that solves problems or understands concepts by comparing the similarities between different things. This kind of thinking helps to apply known solutions to new problem situations.

[0100] The idea of ​​combining numbers and shapes: The idea of ​​combining numbers and shapes is a way of thinking that combines numbers and geometric shapes to solve problems. It uses graphics to intuitively display the relationship between numbers, which helps to understand and solve complex mathematical problems.

[0101] Mathematical modeling thinking: Mathematical modeling thinking is a way of thinking that uses mathematical language and tools to abstract and simulate real-world problems. This thinking analyzes and solves practical problems by building models and is widely used in science, engineering, economics and other fields.

[0102] Whole-part thinking: Whole-part thinking is a way of thinking that solves problems by analyzing the relationship between the overall structure and local details. It emphasizes considering the overall coordination and consistency while solving local problems.

[0103] Classification discussion thinking: Classification discussion thinking is a way of thinking that divides complex problems into several different situations and discusses and solves them separately. It ensures that the solution to the problem is comprehensive and accurate through detailed analysis of different situations.

[0104] Policies that cannot be defined are marked as unknown.

[0105] The specific marking information is shown in Table 1.

[0106] Table 1 Solution strategy annotation

[0107] Solving strategy id Solving strategy name 0 unknown 1 Functional thinking 2 Extreme Thinking 3 Reductionist Thought 4 Analogy thinking 5 The idea of ​​combining numbers and shapes 6 Mathematical modeling ideas 7 Overall and local thinking 8 Classification discussion ideas

[0108] The above 9 solution strategies constitute a set of solution strategies. Each strategy represents the mathematical idea or method used in solving a math problem. When experts annotate each exercise resource, they try to find the closest solution idea as closely as possible according to the explanation of the idea. If there are multiple solution strategy combinations for a problem, they are sorted in the order of solving the problem. Finally, the solution strategy names of all math resources are combined into a CSV file. Each row of the table records the number of a math resource and the solution strategy corresponding to the resource. This CSV file is the data needed to finally construct the solution strategy coordination matrix, in preparation for subsequent cognitive diagnosis and personalized resource recommendation.

[0109] 1.1.4 Solution strategy coordination matrix construction

[0110] In the step of constructing the coordination matrix, we first need to obtain the quantitative relationship between the solution strategies. The specific steps of solving the relationship are as follows:

[0111] Data preparation: There are 9 problem solving strategies in total.

[0112] Count the number of times strategies with serial numbers x and y appear together, that is, the number of co-occurrences :For each pair of solution strategies and , and count the number of times they appear together in all exercise resources.

[0113] Count the number of times a strategy appears alone and :For the solution strategy , count the total number of times it appears in all exercise resources , for the solution strategy , and also count the total number of times it appears in all exercise resources .

[0114] Calculate co-occurrence probability and the probability of occurrence alone , : Co-occurrence probability , is the number of times the two solution strategies appear together, is the maximum number of occurrences, i.e. the total number of exercise resources; the probability of a single occurrence and Respectively represent the solution strategies and Probability of appearing alone.

[0115] Calculate PMI (Pointwise Mutual Information): PMI is an indicator used to measure the correlation between two random events. Calculation solution strategy and PMI value:

[0116] (2)

[0117] Generate a fitness matrix, such as Figure 3 shown.

[0118] The purpose of generating a fit matrix is ​​to quantify the degree of association between different solution strategies. By counting the number of times they appear together and individually in the exercise resources, and calculating the probability of co-occurrence and the probability of individual occurrence, the PMI value is calculated to build a quantitative relationship between the solution strategies. The fit matrix makes it easier to understand the association between solution strategies and provides an important reference for subsequent exercise resource recommendations.

[0119] 1.2 Knowledge Concept Importance Measurement Based on TF-IDF

[0120] By extracting and manually annotating mathematical expressions, each exercise resource contains a different number of mathematical expressions, so the number of knowledge concepts extracted from each exercise resource is also different, and there is a certain degree of repetition. The present invention needs to select the most effective part from these attributes to eliminate repetition and redundancy, thereby further improving the accuracy of exercise recommendation.

[0121] Information gain is a measurement method used for feature selection. By calculating information gain, we can screen out key features that are representative of the exercise resources, while eliminating redundant and irrelevant features that have little impact on the exercise resources.

[0122] The TF-IDF (Term Frequency-Inverse Document Frequency) algorithm is a method for weighting words in a text, and is commonly used in the fields of information retrieval and text mining. The core is to evaluate the importance of a word to the current document by calculating the frequency (TF) of a word in the current document and the inverse document frequency (IDF) in the entire document collection.

[0123] The working process of TF-IDF algorithm is as follows:

[0124] Term Frequency (TF): Indicates the frequency of a term in the current document. The calculation formula is the number of times a term appears in the current document divided by the total number of terms in the current document. If a term appears multiple times in the current document, it means that it is more important in the current document.

[0125] Inverse Document Frequency (IDF): Indicates the importance of a word in the entire document collection. The calculation formula is the total number of documents divided by the logarithm of the number of documents containing the word. If a word rarely appears in the entire document collection, but appears frequently in the current document, it means that it has a strong ability to distinguish the current document.

[0126] TF-IDF value: Combine TF and IDF to calculate the TF-IDF value of the current word. The formula is TF multiplied by IDF. The higher the TF-IDF value, the more important the word is to the current document.

[0127] In the present invention, the TF-IDF algorithm is used to weight knowledge concepts and evaluate their importance in the current resource. For a knowledge concept, if its frequency of appearance in the current exercise resource is high (TF is large), but its frequency of appearance in other exercise resources is low (IDF is large), it means that this knowledge concept is unique and important to the current resource, so its TF-IDF value is high.

[0128] By applying the TF-IDF (Term Frequency-Inverse Document Frequency) algorithm, the knowledge concepts in the exercise resources can be effectively sorted, thereby selecting the most representative knowledge concepts as the salient features of the resource. This method aims to maximize the representative relationship between these knowledge concepts and the current exercise resources, that is, to accurately identify the knowledge concepts that best reflect the uniqueness and recognition of the current resources.

[0129] 1.3 Construction of strategy-level knowledge graph

[0130] 1.3.1 Intra-layer relationship construction:

[0131] When constructing the strategy-level knowledge graph, this implementation method mainly uses the seventh edition of "Advanced Mathematics" compiled by Tongji University, the real questions of the national postgraduate entrance examination in previous years, and the teaching materials for the postgraduate entrance examination as core resources. The entire knowledge graph will be divided into the following three layers:

[0132] 1) Solving the strategy layer:

[0133] According to the mainstream solution strategies in existing advanced mathematics exercises extracted by experts, a knowledge graph was constructed based on the solution strategies, with the solution strategies as the entity set and the degree of coordination between the solution strategies as the relationship set. The degree of coordination is used as the connection relationship between any two solution strategies.

[0134] 2) Exercise resource layer:

[0135] Each math problem resource is considered as an independent entity object. The order in which students learn math resources is considered as the relationship between these entities, and a knowledge graph of the problem resource layer is constructed. Since a single problem resource knowledge graph is difficult to fully display the rich knowledge concepts in the resource, the upper layer is a solution strategy layer with higher-level mathematical semantics, and the lower layer is a knowledge concept layer that describes the characteristics of the problem resource in more detail.

[0136] 3) Knowledge concept layer:

[0137] All knowledge concepts are considered as entity sets, and the relationships between knowledge concepts are considered as the relationship sets of the knowledge graph. As a national planning textbook for undergraduates in general higher education, the relationship between entities is defined based on the prerequisite relationship of knowledge concepts in "Advanced Mathematics" compiled by the Department of Mathematics of Tongji University. Therefore, the knowledge concept entity set and the sequential relationship between knowledge concepts in the knowledge graph are all referenced to this textbook.

[0138] 1.3.2 Construction of inter-layer relationships

[0139] In the previous part, the relationship between layers was mainly introduced. This part defines the inter-layer attribute relationship between the layers of the policy level knowledge graph, as shown in Table 2.

[0140] Table 2 Relationships among multiple layers of knowledge graphs

[0141]

[0142] "Inter-layer attribute relationship" refers to the relationship between the exercise resource layer and the knowledge concept layer and solution strategy layer.

[0143] The constructed strategy-level knowledge graph is as follows: Figure 2 shown.

[0144] 2. Knowledge concept path generation based on knowledge blind spot attributes

[0145] Through cognitive diagnosis by the cognitive diagnosis module, we can obtain the students’ knowledge blind spot attribute set. The knowledge concept learning path of students is generated based on the knowledge blind spot attribute set and the knowledge concept layer knowledge map. The process of generating the path is as follows: Figure 4 As shown, it is carried out in the knowledge concept layer of the strategy-level knowledge graph. In the knowledge concept layer, the path is composed of the previous and next relationships of knowledge concept learning, and there is no cyclic path.

[0146] First, students need to determine the target knowledge concept , ensuring the directionality of the learning path.

[0147] Based on students' historical learning records, the cognitive diagnosis module obtains students' knowledge mastery. In the process of recommending knowledge concept paths, it also takes into account the knowledge concepts that students have already mastered, making the learning path more efficient and accurate.

[0148] When generating knowledge concept paths, the knowledge concept layer of the strategy-level knowledge graph is based on the target knowledge Topological sorting of endpoints to generate dynamic learning paths , Represents the first knowledge concepts, there are a total of A knowledge concept. It is the knowledge concept set of Chapter 0, that is, the knowledge concept set of advanced mathematics. The attributes on the path are filtered and removed. The concept of knowledge in and Represents the number of knowledge concepts in the knowledge concept path before and after shielding. Shielded knowledge concept set After that, get the current learning path ,The final learning path will show in detail the location of the knowledge concepts in the ,learning path, as well as the number of knowledge in the learning path after ,massaging, providing students with clear path planning.

[0149] by Figure 4 For example, the hypergraph cognitive diagnosis model obtains the student's knowledge blind spot set , then the generated knowledge concept learning path is Through the cognitive diagnosis module, the students’ knowledge blind spots are collected, and the acquired knowledge is eliminated to generate a clear knowledge concept learning path.

[0150] 3. Exercise resource path generation based on solution strategy

[0151] Based on the knowledge concept path generated in the previous text , query the exercise resources corresponding to the knowledge concepts on the learning path in the strategy-level knowledge graph ,like Figure 5 For each knowledge concept in the knowledge concept path , query the exercise resources containing the knowledge concept in the exercise resource layer and generate a resource sequence , represents the concept of knowledge The corresponding exercise resources are Here The sequence number of the i-th knowledge concept on the path is , after searching all the knowledge concepts on the path, we can get the exercise resource sequence corresponding to the path , express The exercise resources corresponding to the first knowledge concept are and There are a total of knowledge concepts Corresponding exercise resources. Each exercise resource corresponding to each knowledge concept is selected, and the sub-exercise sequence of each knowledge concept is screened. The screening process is as follows:

[0152] Corresponding exercise resource sequence for knowledge concepts , query all solution strategies contained in the strategy-level knowledge graph for each exercise resource in the sequence, and perform personalized solution strategy tagging on the exercise resource. The process is as follows:

[0153] If the solution strategy corresponding to the exercise resource contains the target solution strategy that the user wants to learn , here It is the abbreviation of target, so use Mark this exercise resource.

[0154] If the solution strategy corresponding to the exercise resource does not include the target solution strategy, then compare the compatibility of all the included solution strategies with the target solution strategy, and find the solution strategy with the highest compatibility based on the PMI value. , mark the problem according to the number of the solution strategy in the matrix , the degree of fit matrix is Figure 3 shown.

[0155] 1. Get the solution strategy tag of the corresponding exercise resource sequence of the current knowledge concept, and retain all and mark the remaining Exercise resources are based on Sort by size.

[0156] 2. Select resources: For this knowledge point, if there is a tag , then all such exercises are retained directly, and the screening of corresponding exercise resources for this knowledge concept is completed; if there is no exercise marked as , then select the sorted mark as The first two exercise resources of the exercise resources serve as the corresponding exercise resources for this knowledge concept.

[0157] 3. Repeat steps 1 to 2 above for each knowledge concept to get the final exercise resource sequence .

[0158] The main purpose of this step is to query the exercise resources related to the knowledge concepts on the path in the exercise resource layer in the strategy-level knowledge graph according to the knowledge concept learning path, and then mark and filter the exercise resource sequence of each knowledge concept to generate the final exercise resource sequence to be recommended.

[0159] In order to more clearly illustrate the effect of the technical solution of the present invention, a specific experiment is given below.

[0160] This experiment aims to systematically explore the performance of the PSS method (personalized exercise resource recommendation method based on solution strategy) under experimental conditions, involving experimental design, data set selection, experimental environment configuration, selection of comparison methods, clarification of evaluation criteria and comprehensive analysis of experimental results. The data set used in the experiment is derived from actual application scenarios, ensuring the practical significance of the research and the authenticity of the data. In the selection of comparison methods, this study fully considered the diversity and practicality of recommendation systems, and finally selected three algorithms with significant representativeness and wide applicability, namely content-based recommendation methods, knowledge-based recommendation algorithms and user-self-learning recommendation algorithms, as controls. By comparing these algorithms with the PSS method, the purpose is to comprehensively evaluate the advantages and disadvantages of the PSS method in recommendation effects. In terms of evaluation methods, this experiment uses a variety of statistical and empirical methods. First, the box plot of the pre- and post-test scores intuitively shows the improvement of the PSS method in learning effects, providing users with an intuitive feeling of performance improvement. Secondly, the T test is used to perform statistical analysis on the experimental data, and the effectiveness of the PSS method in improving recommendation effects is verified from a statistical perspective. Finally, user satisfaction feedback on the PSS method was collected through a questionnaire survey to further evaluate its practicality and user acceptance in practical applications.

[0161] Experimental design

[0162] This experiment invited 80 undergraduate students from our school who have completed the advanced mathematics course to evaluate the impact of different recommendation algorithms on students' knowledge mastery. These students were evenly divided into four groups of 20 people based on their pre-test scores to ensure that each group contained students with different levels of knowledge mastery to control variables. In the experiment, Group A served as the experimental group, and students will study according to the learning resources recommended by the PSS method; while Groups B, C, and D served as the control group, using student self-study, knowledge-based recommendation algorithms, and content-based recommendation algorithms for learning, respectively. In view of the complexity of advanced mathematics, this experiment focused on the 9 core knowledge concepts in the first chapter and provided students with a total of 221 related mathematical resources for learning.

[0163] The experiment was divided into four phases:

[0164] 1) Pre-test stage: To ensure the standardization and timeliness of the test, all students must choose to complete the test questions for two consecutive hours within two days after the pre-test questions are released. After the test, the expert team will strictly review the answers to ensure the fairness and accuracy of the scoring. At the same time, students will be given the right to view their own answer results and the official reference answers to the questions in order to conduct self-assessment and consolidate knowledge.

[0165] 2) Recommendation stage: In this stage, based on the students' pre-test performance, the recommendation algorithm is used to accurately recommend corresponding exercise resources to each student. Students in each group strictly follow the recommendation algorithm of their group and study exercise resources for a week. In this learning process, students can not only deeply understand the knowledge concepts through the recommended exercise resources, but also understand and learn the corresponding solution strategies by observing the exercise solution process.

[0166] 3) In the post-test phase, an assessment mechanism was designed to match the pre-test phase. Specifically, within two days after the pre-test exercises were released, students were required to freely choose a continuous two-hour period to complete a set of exercises that were consistent with the pre-test exercises in terms of knowledge concepts. This design was designed to ensure accurate follow-up assessment of students' mastery of specific knowledge concepts.

[0167] 4) Evaluation phase: After two rounds of tests (pre-test and post-test) and one round of learning, in order to collect students' feedback on the learning system and its effects, this experiment organized group A students to participate in a system satisfaction survey. The survey focused on three main aspects: first, the satisfaction evaluation of the exercise resources recommended by the system, second, the students' mastery of knowledge points and solution strategies before and after the recommended learning, and third, the evaluation of the system page.

[0168] 1.1.1 Control group design

[0169] As described in the above section, Groups B, C, and D were all used as the control groups of this experiment. The experiments were designed using their respective recommended methods in order to conduct comparative analysis with Group A:

[0170] 1) Group B: Students can freely choose the group. The system will only provide students with the exercise resources of Chapter 1 as a question bank. Students choose 15 questions to study. Students should complete the study within one week.

[0171] 2) Group C: Recommendation based on knowledge. According to the answers of students in the pre-test stage, the questions that students answered incorrectly are used as target exercise resources. Knowledge concepts are extracted from the target exercise resources to obtain the knowledge concept set that needs to be mastered. Exercise resources containing this knowledge concept are screened, and the 15 recommended exercise resource sets with the highest matching degree are screened out as the recommended exercise resources for Group C students to study. Students should study the exercises within one week of their release.

[0172] Group D: Content-based recommendation. According to the students' answers, the questions that the students answered incorrectly are used as target exercise resources. The model of chinese-bert-wwm-ext is used as the pre-trained BERT model to match and filter each target exercise resource to obtain the most similar exercise resources as recommended exercises. The recommended exercise set does not exceed 15 exercise resources. The model uses a 12-layer Transformer Encoder with a hidden layer size of 768. Exercise resources and The similarity is calculated using the Pearson correlation coefficient, as shown in formula (3). , Indicates the output vector of the exercise resource after the BERT model is applied. The value of the dimension, Take 768, , Represents the mean of the output vector.

[0173] (3)

[0174] 1.1.2 Experimental Configuration

[0175] This system is built on PyTorch, and the backend service is implemented based on the Spring Boot framework to provide stable and scalable server-side functions. The front-end interaction layer uses the jQuery framework. In terms of data storage, this system chooses the relational database MySQL to support efficient data storage and query. For specific experimental environment configuration, see Table 3 Experimental Environment Configuration Table for details, and the system environment configuration is listed in Table 4 System Environment Configuration Table.

[0176] Table 3 Experimental environment

[0177] Experimental environment Environment Configuration Operating platform Win10, 64-bit CPU AMD Ryzen 7 5800X 8-Core Processor GPU NVIDIA GeForce RTX 3070 Memory 32GB DDR4 programming language Python 3.8.10 Open Source Framework Pytorch 1.10.0 CUDA Version 11.3

[0178] Table 4 System environment

[0179] System environment Environment Configuration Operating platform Win10, 64-bit programming language Java, JavaScript V8, HTML5, CSS3 Backend programming environment IDEA2022.3.3 Server Framework Springboot Front-end programming environment Visual Studio Code 1.77.3 database MySQL 8.0.28

[0180] 1.1.3 Evaluation Metrics

[0181] This experiment has the following assumptions for the PSS algorithm:

[0182] I. The PSS-based recommendation algorithm is more effective than the control group;

[0183] II. Experimental group A is more satisfied with the online learning system;

[0184] For the proposed hypothesis, we set corresponding evaluation indicators to verify its authenticity. These indicators help us systematically analyze the experimental results, including:

[0185] I. Algorithm Validity

[0186] Box plot: A graph based on the five key characteristic values ​​of a set of data, namely the maximum value, the minimum value, the median and the two quartiles. The main purpose of this graph is to intuitively display the distribution of the original data. In the study of the present invention, a box plot is used to intuitively display the data distribution of the four groups of pre- and post-test score samples, and in this way, the differences between the data distribution characteristics of each group are deeply analyzed.

[0187] (2) Independent samples Test: Independent Samples The test is a statistical method that aims to evaluate whether there is a significant difference between two groups of samples from a normal distribution on a specific indicator. In this experimental study, the independent sample test will be used to test whether the changes in the scores of students in different groups between the pre-test and post-test stages are significant, so as to evaluate whether there are significant differences in their learning effects.

[0188] Data Group and The assumptions for the score differences are as follows:

[0189] : and The difference in scores was not significant;

[0190] : and The scores differed significantly;

[0191] set up The number of students in the group is The average score is , the standard deviation is ; The number of students in the group is The average score is , the standard deviation is . The value calculation is shown in formula (4):

[0192] (4)

[0193] The degrees of freedom (df) are calculated as shown in formula (5):

[0194] (5)

[0195] The difference is calculated using Cohen's d, as shown in formula (6). , then the difference between the two groups of data is not statistically significant, belonging to the category of small effect, and the difference between the two groups is not large; if , then the difference between the two groups of data is statistically significant, belonging to the medium effect category, and there is a difference between the two groups; if , then the difference between the two groups of data is statistically significant and belongs to the category of large effect, and the difference between the two groups is large;

[0196] (6)

[0197] The p-value is based on The significance level is 0.05. If the p value is less than or equal to 0.05, the hypothesis is rejected. Assume, accept Assume that there is a significant difference in the scores of the two groups of students.

[0198] In this study, given the small number of samples in each group, it is crucial to ensure that the results of the independent sample test are statistically reliable. In order to verify whether the sample data conforms to the normal distribution, a normality test method specifically for small samples was selected - the Shapiro-Wilk normality test (W test for short). This method was proposed by Shapiro.SS and Wilk.MB in 1965. Compared with other normality tests, such as the Anderson-Darling test or the Kolmogorov-Smirnov test, the W test has higher sensitivity and accuracy under small sample conditions. Therefore, in order to accurately evaluate whether the pre- and post-test scores of the four groups of students conform to the normal distribution, the W test was selected as the preferred method for the small sample normality test in this study.

[0199] The W test assumptions are as follows:

[0200] : The sample data is approximately normally distributed;

[0201] :The sample data does not satisfy the approximate normal distribution.

[0202] If the p-value is less than 0.05, the null hypothesis is rejected and the sample data is considered to be normally distributed; otherwise, the sample data is considered to be not normally distributed.

[0203] In order to comprehensively evaluate students' satisfaction with the online learning system, a survey was conducted from two key dimensions: one is satisfaction with the recommendation algorithm, and the other is satisfaction with the overall use of the system. After completing the post-test, students in the experimental group will be invited to fill out a satisfaction questionnaire. This questionnaire is anonymous and non-compulsory, and is designed to encourage students to truly feedback their personal feelings. The questionnaire design uses a Likert scale, and each question has five options, including "strongly disagree", "disagree", "uncertain", "agree" and "strongly agree". Students can choose the option that best suits their own views based on their actual usage experience and feelings.

[0204] Comparative experiment and result analysis

[0205] I. PSS algorithm effectiveness verification

[0206] (1) Box plot test

[0207] The pre-test and post-test score data of students in groups A, B, C and D are plotted to show their distribution characteristics. Figure 6 shown.

[0208] After careful analysis, we can observe that in the pre-test stage, the average scores of each group were quite close, indicating that there were students with different cognitive abilities in each group. However, after the learning phase of the specific recommendation algorithm, the cognitive abilities of all students were enhanced, showing significant progress. In particular, Group A had a significant leap in its post-test scores compared to the pre-test stage. Specifically, the average score of Group A increased from 5.0 to 7.5, and the median also jumped from 5.0 to 8.0, which was the most significant increase among the four groups. This significant change shows that the personalized recommendation system using the PSS algorithm has played a positive role in improving students' cognitive abilities. In the post-test stage, the average score of Group A was 2.3 points higher than that of Group B, 2 points higher than that of Group C, and 2.3 points higher than that of Group D, further confirming the effectiveness of the PSS algorithm in the field of personalized recommendation.

[0209] The experimental results show that the overall cognitive ability of the students in the experimental group has been significantly improved, and the personalized learning resource recommendation algorithm has a particularly significant impact on the overall cognitive state of students. By using a personalized recommendation algorithm, it is possible to more accurately match students' learning needs and characteristics, provide more targeted learning resources, and thus promote the development of students' cognitive abilities.

[0210] (2) Independent samples test

[0211] First, a W test was performed on the two test scores of groups A, B, C, and D. The results are shown in Table 5.

[0212] Table 5 W test

[0213]

[0214] The analysis of the experimental results shows that the p-values ​​of the four groups in the pre-test and post-test stages are all greater than 0.05. Therefore, the null hypothesis is accepted: the performance data presents an approximately normal distribution. Therefore, in order to verify whether the scores of different groups in the pre-test and post-test stages are significantly different, an independent sample test can be performed on these data. The analysis results are shown in Table 4.

[0215] Table 6 shows that in the pre-test phase, ,accept and The difference in scores was not significant; there was no significant difference in scores between each group. In the pre-test phase, the experiment successfully controlled the students' score variables to ensure that the ability levels of students in each group were roughly the same. However, in the post-test phase, the scores of Group A and the control groups were different. , reject ,accept and The score difference is significant; the results show that there is a significant difference in scores between Group A and the control groups in the post-test stage, and the difference d is more than 0.9. This result shows that compared with the recommendation algorithm used by the control group, the personalized exercise resource recommendation algorithm used by Group A has obvious advantages in improving students' cognitive abilities.

[0216] Table 6 Independent Samples Test

[0217]

[0218] right Figure 7 From the data analysis, we can see that Group A achieved the highest score in the post-test phase, significantly ahead of the other control groups. At the same time, although Groups B, C, and D had a certain increase in scores compared to the pre-test phase, in the comparison between them, the statistical test showed ,accept Therefore, the difference in scores between them is not statistically significant, and both are significantly lower than Group A. Although the recommendation algorithm of the control group can promote the improvement of students' scores to a certain extent, its improvement and effect are lower than the personalized exercise resource recommendation method adopted by Group A. Therefore, it can be concluded that the recommendation algorithm of Group A shows more significant and effective advantages in improving students' cognitive abilities.

[0219] Further in-depth analysis of the reasons for the significant difference in scores between the control group and group A in the post-test phase revealed several potential factors. First, group B adopted a method where students freely selected learning resources, which may make it difficult for students to accurately identify their weak knowledge points when faced with a large number of resources, and spend a lot of time in the process of screening and browsing resources, thus reducing learning efficiency and student enthusiasm. Without clear guidance, students often find it difficult to quickly and effectively select appropriate learning resources for specific knowledge points.

[0220] For Group C, although it adopted a knowledge-based learning resource recommendation method, this recommendation was mainly based on the knowledge concepts in the exercise resources that students answered incorrectly. However, this method may ignore the actual problem-solving strategies that students need to master in the problem-solving process, and it does not fully consider the students' existing cognitive level. Therefore, students may only be able to learn the knowledge fragments related to the wrong answers, and cannot systematically improve their problem-solving ability and cognitive level.

[0221] As for Group D, it adopted a content-based recommendation algorithm. Although this method can recommend resources based on the similarity of text semantics, it may also lead to a lack of diversity in resources due to over-reliance on semantic similarity. Students may therefore be restricted to a way of thinking under specific conditions and fail to gain a broader and deeper cognitive improvement. In addition, since it is difficult for the model to truly understand the complexity and variability of mathematical semantics, its recommendation effect may be significantly affected when the semantics change significantly.

[0222] II. Verification of Satisfaction with the Online Learning System

[0223] This part invites 20 students in Group A to participate in the online learning system satisfaction survey, and finally collects 17 questionnaire results. Five different levels of options are used to measure student satisfaction. Five hypotheses are designed respectively:

[0224] A: Improve your knowledge level and problem-solving ability.

[0225] B: The exercise resources provided in this experiment are in line with my own learning situation.

[0226] C: Focusing on improving problem-solving strategies is more effective in learning knowledge.

[0227] D: The difficulty of the recommended exercises increases from easy to difficult, which conforms to the objective laws of learning.

[0228] E: In future studies, I will also focus on improving my problem-solving strategies to learn advanced mathematics.

[0229] F: The content has a high degree of overlap with the knowledge points tested in the incorrect questions in the previous test.

[0230] (1) Survey on satisfaction with the PSS algorithm, such as Figure 7 shown.

[0231] As can be seen from the figure, except for a very small number of students who are uncertain about the effectiveness of the recommendation algorithm, students are generally satisfied with the system's recommendation algorithm. Among them, 10 students believe that the learning content recommended by the system can effectively improve their knowledge mastery and problem-solving ability. Most students are very convinced that they will also use the focus on improving the ability to use problem-solving strategies to learn advanced mathematics in the future. This is due to the solution strategy-based approach in the recommendation algorithm, which can mine a large amount of knowledge related to knowledge concepts that students have not mastered, making it easier for students to master the solution strategies frequently used in the solution process, thereby effectively improving students' problem-solving ability and improving students' scores.

[0232] Most students think that the recommended learning content is of appropriate difficulty, the questions are suitable for the students' level, they are satisfied with their knowledge improvement, and will use this method to learn advanced mathematics in the future. Therefore, the student satisfaction with the PSS method proposed in the present invention is relatively high.

[0233] (2) System satisfaction survey, such as Figure 8 As shown:

[0234] From the analysis of the survey results, all the interviewed students gave positive comments on the comprehensiveness and ease of use of the system functions, indicating that the system design meets the basic needs of users and has a good user experience. Furthermore, most students expressed their expectations for the future launch of the system, which reflects their confidence and expectations for the long-term operation of the system. 14 students explicitly stated that they would recommend the system to their friends, which further strengthened the positive reputation of the system among the student group. However, it is worth noting that some students still have reservations about whether to continue to use the system in the future and whether to recommend it to others. This uncertainty may be due to the specific background of the student group, that is, they are mainly sophomores in non-mathematics majors. For these students, advanced mathematics is not the core content of their majors. Therefore, if there is no further need for further study, they may not conduct in-depth research on advanced mathematics, which will affect their willingness to continue using the system.

[0235] In general, through the above real experiments, a comprehensive comparison and analysis of various learning methods such as content-based recommendation, knowledge-based recommendation and student autonomous learning was conducted. In the experiment, the PSS method proposed in this invention was used, and its performance in recommendation effect was compared. The experimental results show that the PSS method has shown good performance in multiple evaluation indicators, significantly better than other traditional recommendation methods.

[0236] Furthermore, in order to evaluate the effect of the PSS method in practical applications, students in the experimental group were invited to participate in a questionnaire and their satisfaction data on various learning methods were collected. Through rigorous experimental design and data analysis, the advantages of the PSS method in terms of recommendation effect and student satisfaction were verified.

[0237] Embodiment 2

[0238] Based on the same inventive concept, this embodiment discloses a personalized exercise resource recommendation system based on a solution strategy, including:

[0239] The cognitive status diagnosis module is used to analyze the learner's feedback data and learning behavior to obtain the learner's knowledge blind spot set;

[0240] The knowledge graph construction module is used to extract metadata to construct a strategy-level knowledge graph, where the metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer uses solution strategies as entities, and the degree of association between solution strategies as the relationship between entities. The problem resource layer uses each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer uses each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer.

[0241] The knowledge concept learning path generation module is used to obtain the target knowledge concept according to the knowledge blind spot set or the selection of the target knowledge concept. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced by topological sorting to generate a knowledge concept learning path that takes into account the logical order and difficulty of knowledge.

[0242] The exercise resource recommendation module is used to generate a sequence of exercise resources to be recommended based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer.

[0243] Since the system introduced in the second embodiment of the present invention is a system used to implement the personalized exercise resource recommendation method based on the solution strategy in the first embodiment of the present invention, based on the method introduced in the first embodiment of the present invention, the person skilled in the art can understand the specific structure and deformation of the system, so it is not repeated here. All systems used in the method in the first embodiment of the present invention belong to the scope of protection of the present invention.

[0244] Embodiment 3

[0245] Based on the same inventive concept, the present invention further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the method described in the first embodiment is implemented.

[0246] Since the computer-readable storage medium introduced in the third embodiment of the present invention is the computer-readable storage medium used to implement the personalized exercise resource recommendation method based on the solution strategy in the first embodiment of the present invention, based on the method introduced in the first embodiment of the present invention, the person skilled in the art can understand the specific structure and deformation of the computer-readable storage medium, so it is not repeated here. All computer-readable storage media used in the method of the first embodiment of the present invention belong to the scope of protection of the present invention.

[0247] Embodiment 4

[0248] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method described in Embodiment 1 when executing the program.

[0249] Since the computer device introduced in the fourth embodiment of the present invention is a computer device used to implement the personalized exercise resource recommendation method based on the solution strategy in the first embodiment of the present invention, based on the method introduced in the first embodiment of the present invention, the person skilled in the art can understand the specific structure and deformation of the computer device, so it is not repeated here. All computer devices used in the method of the first embodiment of the present invention belong to the scope of protection of the present invention.

[0250] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0251] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0252] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic creative concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A personalized exercise resource recommendation method based on solution strategy, characterized in that: include: Analyze learners' feedback data and learning behaviors to obtain learners' knowledge blind spots. Extract metadata to construct a strategy-level knowledge graph, where metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer takes the solution strategy as an entity, and the degree of association between solution strategies as the relationship between entities. The problem resource layer takes each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer takes each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer. According to the knowledge blind spot set or the selection of the target knowledge concept, the target knowledge concept is obtained. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced using topological sorting to generate a knowledge concept learning path that takes into account the logical order and difficulty of knowledge. Generate a sequence of exercise resources to be recommended based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer; Among them, extracting metadata to build a strategy-level knowledge graph includes: Collect math problem resources, extract and annotate the knowledge concepts and solution strategies in the math problem resources, calculate the degree of fit between the two strategies based on the probability of a solution strategy appearing alone in a math problem resource and the probability of two different solution strategies appearing together in the same math problem resource, and obtain a fit matrix, where the elements in the fit matrix are used to measure the degree of association between the two solution strategies; Based on the TF-IDF algorithm, the knowledge concepts in the math problem resources are weighted to determine the importance of the knowledge concepts; The knowledge concept layer is constructed according to the extracted and labeled knowledge concepts and the importance of the knowledge concepts. The solution strategy layer is constructed according to the labeled solution strategies and the coordination matrix. The exercise resource layer is constructed according to the exercise resources and the learning order of the exercise resources.

2. The method for recommending personalized exercise resources based on solution strategies as claimed in claim 1, characterized in that: The marked solution strategies include: function thinking, limit thinking, reduction thinking, analogy thinking, number-shape combination thinking, mathematical modeling thinking, whole-part thinking, classification discussion thinking and unknown type thinking.

3. The method for recommending personalized exercise resources based on solution strategies as claimed in claim 1, characterized in that: The learner's knowledge blind spot set includes knowledge concepts that the learner has not mastered. According to the knowledge blind spot set or the selection of the target knowledge concept, the target knowledge concept is obtained, including: If the learner has selected the knowledge concept to be learned, the selected knowledge concept is used as the target knowledge concept; otherwise, the last knowledge concept in the knowledge blind spot set is used as the target knowledge concept.

4. The method for recommending personalized exercise resources based on solution strategies as claimed in claim 1, characterized in that: Based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer, a sequence of exercise resources to be recommended is generated, including: In the exercise resource layer of the strategy-level knowledge graph, all exercise resources that have a mapping relationship with the knowledge concepts included in the knowledge concept learning path are searched; Based on the mapping relationship between the exercise resource layer and the solution strategy layer, the queried exercise resource sequence is mapped to the solution strategy layer, and the exercise resources corresponding to the solution strategy with the highest degree of coordination with the target solution strategy are screened out; According to the learning order of knowledge concepts, multiple corresponding exercise resource sequences are sorted, and finally a sequence of exercise resources to be recommended is generated.

5. The method for recommending personalized exercise resources based on solution strategies as claimed in claim 4, characterized in that: Based on the mapping relationship between the exercise resource layer and the solution strategy layer, the queried exercise resource sequence is mapped to the solution strategy layer, and the exercise resources corresponding to the solution strategy with the highest degree of coordination with the target solution strategy are screened out, including: Personalized solution strategy marking for exercise resources, including: obtaining all solution strategies of exercise resources that have a mapping relationship with the knowledge concepts in the knowledge concept learning path, judging whether all solution strategies contain the target solution strategy that the user wants to learn, and if so, using Mark this exercise resource, where Represents exercise resources, represents the target solution strategy, express Otherwise, compare the correlation between all solution strategies and the target solution strategy, and find the solution strategy with the highest correlation with the target solution strategy according to the matching value. ,according to The problem resource is marked with the number of the solution strategy in the fitness matrix , Represents a solution strategy and The compatibility value of For all marked exercise resources, mark them with The exercise resources are retained, and other exercise resources are Sort by size and keep The exercise resource with the largest value is selected, and the rest are deleted. The exercise resources retained are the exercise resources corresponding to the solution strategy with the highest degree of fit with the target solution strategy.

6. A personalized exercise resource recommendation system based on solution strategies, characterized by: include: The cognitive status diagnosis module is used to analyze the learner's feedback data and learning behavior to obtain the learner's knowledge blind spot set; The knowledge graph construction module is used to extract metadata to construct a strategy-level knowledge graph, where the metadata includes various math problem resources. The strategy-level knowledge graph includes a solution strategy layer, a problem resource layer, and a knowledge concept layer. The solution strategy layer uses solution strategies as entities, and the degree of association between solution strategies as the relationship between entities. The problem resource layer uses each math problem resource as an entity, and the learning order of math problem resources as the relationship between entities. The knowledge concept layer uses each knowledge concept as an entity, and the relationship between knowledge concepts as the relationship between entities. There is a mapping relationship between the problem resource layer, the knowledge concept layer, and the solution strategy layer. The knowledge concept learning path generation module is used to obtain the target knowledge concept according to the knowledge blind spot set or the selection of the target knowledge concept. In the knowledge concept layer of the hierarchical knowledge graph, the target knowledge concept is used as the end point, and the dependency relationship between the knowledge concept layers in the strategic hierarchical knowledge graph is reversely traced by topological sorting to generate a knowledge concept learning path that takes into account the logical order and difficulty of knowledge. An exercise resource recommendation module, for generating an exercise resource sequence to be recommended based on the generated knowledge concept learning path, the mapping relationship between the exercise resource layer and the knowledge concept layer, and the mapping relationship between the exercise resource layer and the solution strategy layer; Among them, the knowledge graph construction module is specifically used for: Collect math problem resources, extract and annotate the knowledge concepts and solution strategies in the math problem resources, calculate the degree of fit between the two strategies based on the probability of a solution strategy appearing alone in a math problem resource and the probability of two different solution strategies appearing together in the same math problem resource, and obtain a fit matrix, where the elements in the fit matrix are used to measure the degree of association between the two solution strategies; Based on the TF-IDF algorithm, the knowledge concepts in the math problem resources are weighted to determine the importance of the knowledge concepts; The knowledge concept layer is constructed according to the extracted and labeled knowledge concepts and the importance of the knowledge concepts. The solution strategy layer is constructed according to the labeled solution strategies and the coordination matrix. The exercise resource layer is constructed according to the exercise resources and the learning order of the exercise resources.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the personalized exercise resource recommendation method based on solution strategy as described in any one of claims 1 to 5 is implemented.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the personalized exercise resource recommendation method based on solution strategy as described in any one of claims 1 to 5 is implemented.

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