Mathematical question and answer process teaching system and method thereof

Abstract

The invention provides a mathematical question and answer process teaching system, which comprises a user interaction module, a question analysis and standardization module, a cognitive diagnosis engine, a generative teaching module, a mathematical knowledge graph database and a user portrait database, teaching content and guiding questions are presented to the user in a multi-mode form; the question analysis and standardization module is used for performing semantic understanding and structured analysis on mathematical questions and generating standardized question description and at least one standard question solving path; according to the method, the structured reasoning of the knowledge graph is combined with the natural language generation ability of the generative AI, so that a closed loop from'problem solving 'to'diagnosis' to'heuristic teaching 'is realized, thinking blockage points of students can be accurately positioned and personalized tutoring can be provided like human teachers, and the learning efficiency and the autonomous thinking ability are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of teaching system technology, and in particular to a teaching system and method for mathematical problems and solutions. Background Technology

[0002] Mathematics education is a key link in cultivating students' logical thinking and problem-solving abilities. With the rapid development of information technology, intelligent education systems have emerged, aiming to assist or even replace some traditional teaching functions.

[0003] Currently, mathematics teaching products on the market can be mainly classified into three categories: The first category is online problem-solving tools, such as Photomath and WolframAlpha. These tools can quickly provide the final answer and fixed solution steps for math problems through image recognition or text input. Their core technology lies in symbolic computation and pattern matching. However, the shortcomings of these tools are obvious: they provide a "black box" and one-way knowledge transmission. Users can only passively receive the results. The system cannot understand the user's thought process. When the user's problem-solving ideas deviate from the preset single path, the system cannot provide effective help, let alone cultivate the user's thinking ability.

[0004] The second category is online course and question bank platforms, such as Khan Academy and Yuanfudao. These platforms provide a large number of structured teaching videos and practice questions, forming a rich knowledge resource library. However, their content is pre-made and static, lacking the ability to adjust dynamically in real time. They cannot generate targeted tutoring content in real time based on the specific and instantaneous cognitive weaknesses exposed by users in the process of solving problems. Their personalization level remains at the shallow stage of "recommending related questions".

[0005] The third category is traditional intelligent tutoring systems. These systems are typically based on cognitive psychology theories and computer modeling, attempting to simulate the tutoring process of human teachers. They usually have a built-in "domain model" (subject knowledge), a "student model" (student status), and a "teaching model" (teaching strategies). However, the construction and maintenance costs of these systems are extremely high. Their "student model" and "teaching model" rely on a large number of manually written rules, making it difficult to cover the ever-changing error types and problem-solving approaches in mathematics. Their feedback language is often mechanical and rigid, lacking the inspiration and flexibility of real teaching interactions.

[0006] In summary, existing technologies generally suffer from one or more of the following technical bottlenecks: Insufficient depth of cognitive diagnosis: Most of the time, it remains at the surface level of judging whether the steps are right or wrong, and cannot penetrate the phenomenon to dig out the deeper reasons hidden behind the error.

[0007] The teaching is not interactive or inspiring: it is mostly one-way information transmission, lacks effective two-way interaction, cannot guide students to conduct inquiry-based learning, and is difficult to stimulate their independent thinking.

[0008] Poor personalization and adaptability: The teaching content and strategies are rigid and cannot provide a dynamic teaching plan that is "personalized" for each student based on their unique cognitive state and learning style. To address this, a teaching system and method for mathematical problems and solutions are proposed. Summary of the Invention

[0009] In view of this, embodiments of the present invention provide a teaching system and method for mathematical problems and solutions, in order to solve or alleviate the technical problems existing in the prior art, and at least provide a beneficial option.

[0010] The technical solution of this invention is implemented as follows: a teaching system for mathematical problems and solutions, including a user interaction module, a problem analysis and standardization module, a cognitive diagnosis engine, a generative teaching module, a mathematical knowledge graph database, and a user profile database, wherein... The user interaction module is used to receive mathematical problems and solutions input by the user, and to present teaching content and guiding questions to the user in a multimodal format. The problem parsing and standardization module is used to perform semantic understanding and structured parsing of mathematical problems, and generate standardized problem descriptions and at least one standard solution path. The cognitive diagnostic engine is communicatively connected to the question parsing and standardization module. The cognitive diagnostic engine includes a problem-solving path comparison unit, an error classification unit, and a knowledge graph tracing unit. The problem-solving path comparison unit is used to compare the user's problem-solving process sequence with the standard problem-solving path sequence layer by layer, and identify the steps and nodes that differ from each other. The error classification unit is used to label the different step nodes with error types based on a preset error type knowledge base. The error types include at least conceptual errors, calculation errors, and logical errors. The knowledge graph tracing unit is used to trace back along the dependency edges in a pre-built mathematical knowledge graph based on the knowledge points associated with the different step nodes, in order to locate at least one root cause knowledge point that caused the error. The generative teaching module is communicatively connected to the cognitive diagnostic engine, the mathematical knowledge graph database, and the user profile database. The generative teaching module is used to receive the error type and root cause knowledge points output by the cognitive diagnostic engine, and to retrieve the user's historical learning data from the user profile database. Based on error type, root cause knowledge points, and user's historical learning data, a dynamic teaching instruction is constructed. Input teaching instructions into a pre-trained generative AI model to generate personalized, heuristic teaching content; The mathematical knowledge graph database stores structured mathematical knowledge points, prerequisite relationships between knowledge points, and common error patterns associated with each knowledge point. The user profile database stores a user's problem-solving history, error records, quantitative values ​​of their mastery of knowledge points, and learning preference tags.

[0011] In some embodiments, the user interaction module supports at least one of the following multimodal inputs: text input, handwritten formula recognition, voice input, and image question recognition; the multimodal outputs include at least one of the following: text, graphics, animation, and voice.

[0012] In some embodiments, the problem-solving path comparison unit uses a sequence matching-based algorithm to calculate the similarity between the user's problem-solving steps and the standard problem-solving steps. When the similarity is lower than a preset threshold, the step is marked as a difference step node.

[0013] In some embodiments, the teaching instructions constructed by the generative teaching module follow the following logical function: Prompt=f(Error_Type,Root_Concept,Student_Profile,Teaching_Strategy) Among them, Prompt is the generated teaching instruction, Error_Type is the error type, Root_Concept is the root cause knowledge point, Student_Profile is the user profile, and Teaching_Strategy is the teaching strategy selected from the preset strategy library. The teaching strategies include Socratic questioning, analogical explanation or visual demonstration.

[0014] In some embodiments, when the Teaching_Strategy is a Socratic question, the teaching content generated by the generative teaching module includes one or more guiding questions, which are designed to construct a cognitive conflict scenario to prompt users to discover and correct their own erroneous logic.

[0015] A method for teaching mathematical problems and solutions includes the following steps: S1. Receive math problems and corresponding solutions submitted by users through the user interaction module; S2. Using the problem analysis and standardization module, the mathematical problem is analyzed, and the core knowledge points associated with the problem and at least one standard solution path are extracted from the mathematical knowledge graph database. S3. Through the cognitive diagnostic engine, the user's problem-solving process is compared with the standard problem-solving path to identify the erroneous steps that differ from the standard. S4. Classify the identified erroneous steps by error type and use mathematical knowledge graphs to trace the root cause knowledge points that led to the error; S5. Combining the error types, root cause knowledge points, and user historical learning data retrieved from the user profile database, construct a personalized teaching instruction. S6. Input the teaching instructions into the generative AI model to generate heuristic teaching content; S7. Through the user interaction module, the generated teaching content is presented to the user, and user feedback is received. The user profile in the user profile database is updated based on the feedback.

[0016] In some embodiments, in S3, the user steps are calculated using the following algorithm formula. With standard procedures similarity : in, and Operators representing user steps and standard steps, respectively. and Represents operands, and These are the similarity functions for operators and operands, respectively. and These are preset weighting coefficients, and When similarity Below a preset threshold If this happens, the step is determined to be an erroneous step.

[0017] In some embodiments, in step S4, the knowledge graph tracing process includes tracing the knowledge point nodes corresponding to the erroneous steps. Let's start with knowledge graphs. Search for all its directly preceding knowledge point nodes in the middle. And based on the historical error frequency in the user profile database, calculate each prerequisite knowledge point. The "suspicion" : in, It is the user's prior knowledge points Historical error frequency It is a smoothing factor used to avoid zero-frequency problems; Select "Suspicion Level" The most important prerequisite knowledge point is the fundamental reason knowledge point.

[0018] The embodiments of the present invention have the following advantages due to the adoption of the above technical solutions: I. This invention combines the structured reasoning of knowledge graphs with the natural language generation capabilities of generative AI to achieve a closed loop from "problem solving" to "diagnosis" and then to "heuristic teaching." Like a human teacher, it can accurately locate students' thinking blockages and provide personalized tutoring, significantly improving learning efficiency and independent thinking ability.

[0019] Second, this invention leverages the powerful language generation and logical reasoning capabilities of generative AI to dynamically generate Socratic questions, vivid analogical explanations, or interactive visual animations based on cognitive diagnostic results and user profiles. This teaching method goes beyond simply providing answers; instead, it inspires and guides students to construct their own correct knowledge systems, effectively cultivating their critical thinking and problem-solving abilities.

[0020] Third, by continuously capturing user feedback on teaching content and dynamically updating the user profile database, this invention enables more accurate subsequent cognitive diagnosis and teaching strategies, forming an adaptive learning closed loop of "real-time diagnosis - dynamic teaching - feedback optimization," making the system "understand" students better the more it is used.

[0021] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a system architecture diagram of the present invention; Figure 2 This is a simplified schematic diagram of the mathematical knowledge graph of this invention. Detailed Implementation

[0024] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0025] It is important to note that terms such as "first," "second," "symmetric," "array," "set in," and "set with" are used only to distinguish between descriptive and positional descriptions and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features specified with terms such as "first" or "symmetric" may explicitly or implicitly include one or more of that feature; similarly, when the quantity of certain features is not limited by words such as "two" or "three," it should be noted that such features also explicitly or implicitly include one or more features.

[0026] In this invention, unless otherwise explicitly specified and limited, terms such as "installation," "connection," and "fixation" should be interpreted broadly; for example, they can refer to a fixed connection, a detachable connection, or an integral molding; they can refer to a mechanical connection, a direct connection, a welding connection, or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the accompanying drawings and specific circumstances.

[0027] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0028] like Figures 1-2 As shown, this embodiment of the invention provides a teaching system for mathematical problems and solutions, including a user interaction module, a problem analysis and standardization module, a cognitive diagnosis engine, a generative teaching module, a mathematical knowledge graph database, and a user profile database. The user interaction module is used to receive math problems and solutions input by users, and to present teaching content and guiding questions to users in a multimodal format. The Problem Analysis and Standardization module is used to perform semantic understanding and structured analysis on mathematical problems, generating standardized problem descriptions and at least one standard solution path; The cognitive diagnostic engine communicates with the question parsing and standardization module. The cognitive diagnostic engine includes a problem-solving path comparison unit, an error classification unit, and a knowledge graph tracing unit. The problem-solving path comparison unit is used to compare the user's problem-solving process sequence with the standard problem-solving path sequence layer by layer to identify the steps and nodes that differ from each other. The error classification unit is used to label the different step nodes with error types based on a pre-defined error type knowledge base. The error types include at least conceptual errors, calculation errors, and logical errors. The knowledge graph tracing unit is used to trace back along the dependency edges in a pre-built mathematical knowledge graph based on the knowledge points associated with the differing step nodes, in order to locate at least one root cause knowledge point that caused the error. The generative teaching module communicates with the cognitive diagnostic engine, the mathematical knowledge graph database, and the user profile database. The generative teaching module is used to receive the error types and root cause knowledge points output by the cognitive diagnostic engine, and to retrieve the user's historical learning data from the user profile database. Based on error type, root cause knowledge points, and user's historical learning data, a dynamic teaching instruction is constructed. Input teaching instructions into a pre-trained generative AI model to generate personalized, heuristic teaching content; The mathematical knowledge graph database stores structured mathematical knowledge points, prerequisite relationships between knowledge points, and common error patterns associated with each knowledge point. The user profile database stores users' problem-solving history, error records, quantitative values ​​of their mastery of knowledge points, and learning preference tags.

[0029] In this embodiment, specifically, the user interaction module supports at least one of the following multimodal inputs: text input, handwritten formula recognition, voice input, and image question recognition; and at least one of the following multimodal outputs: text, graphics, animation, and voice.

[0030] In this embodiment, specifically, the problem-solving path comparison unit uses a sequence matching-based algorithm to calculate the similarity between the user's problem-solving steps and the standard problem-solving steps. When the similarity is lower than a preset threshold, the step is marked as a difference step node.

[0031] In this embodiment, the teaching instructions constructed by the generative teaching module specifically follow the following logical function: Prompt=f(Error_Type,Root_Concept,Student_Profile,Teaching_Strategy) Among them, Prompt is the generated teaching instruction, Error_Type is the error type, Root_Concept is the root cause knowledge point, Student_Profile is the user profile, and Teaching_Strategy is the teaching strategy selected from the preset strategy library. The teaching strategies include Socratic questioning, analogical explanation or visual demonstration.

[0032] In this embodiment, specifically when Teaching_Strategy is a Socratic question, the teaching content generated by the generative teaching module includes one or more guiding questions. The questions aim to construct a cognitive conflict scenario to prompt users to discover and correct their own erroneous logic.

[0033] A method for teaching mathematical problems and solutions includes the following steps: S1. Receive math problems and corresponding solutions submitted by users through the user interaction module; S2. Using the problem analysis and standardization module, analyze the math problem and extract the core knowledge points related to the problem and at least one standard solution path from the math knowledge graph database. S3. Through the cognitive diagnostic engine, the user's problem-solving process is compared with the standard problem-solving path to identify the erroneous steps that differ from the standard. S4. Classify the identified erroneous steps by error type and use mathematical knowledge graphs to trace the root cause knowledge points that led to the error; S5. By combining error types, root cause knowledge points, and user historical learning data retrieved from the user profile database, a personalized teaching instruction is constructed. S6. Input the teaching instructions into the generative AI model to generate heuristic teaching content; S7. Through the user interaction module, the generated teaching content is presented to the user, and user feedback is received. Based on the feedback, the user profile in the user profile database is updated.

[0034] In this embodiment, specifically in S3, the user steps are calculated using the following algorithm formula. With standard procedures similarity : in, and Operators representing user steps and standard steps respectively (such as +, -, *, / , d / dx, ∫). and Represents operands (which can be numbers, variables, or expressions). and These are the similarity functions for operators and operands, respectively. It is the operator similarity, usually a binary function (1 for the same operator, 0 for different operator). It refers to operand similarity, which can be a function based on string similarity or numerical difference, or it can be based on edit distance. and These are preset weighting coefficients, and When similarity Below a preset threshold If the value is 0.7 (e.g., 0.7), the step is considered an error.

[0035] In this embodiment, specifically in S4, the knowledge graph tracing process includes starting from the knowledge point node corresponding to the erroneous step. Let's start with knowledge graphs. Search for all its directly preceding knowledge point nodes in the middle. And based on the historical error frequency in the user profile database, calculate each prerequisite knowledge point. The "suspicion" : in, It is the user's prior knowledge points Historical error frequency It is a smoothing factor used to avoid zero-frequency problems; Select "Suspicion Level" The most fundamental prerequisite knowledge point is taken as the root cause knowledge point; It represents a specific prerequisite knowledge point. The "original suspicion score"; This refers to the current user's historical interactions with knowledge points. Frequency of errors across all related questions; Data source: This value is dynamically derived from the user profile database 106 of this invention; Each time a user completes a practice session and undergoes system diagnostics, their mastery of the corresponding knowledge point is updated. If a user answered 4 out of the last 10 questions involving "absolute values" incorrectly, then... The value of (absolute value) can be recorded as 0.4; If a student repeatedly makes mistakes on a particular knowledge point, it strongly suggests that this knowledge point is a weak link in their cognitive structure. The higher the value, the better. The greater the likelihood that it is the root cause.

[0036] It is a preset positive constant, usually taking a small value, such as 0.5 or 1.0, which is technically known as a variant of Laplace smoothing or plus-one smoothing; The smoothing factor is introduced to address the problems of data sparsity and "zero probability," which occur if a student has never practiced a particular knowledge point. So, its historical error frequency =0; Without a smoothing factor, the system would assume that the knowledge point is perfectly mastered, with zero suspicion, which is obviously unreasonable. It may simply be due to a lack of practice rather than true mastery.

[0037] The introduction of this is similar to the judicial trial process, where even if a suspect has no prior criminal record ( We cannot directly determine his innocence, but rather give him a basic "suspicion score." This basic score ensures that all knowledge points are qualified to be suspected, making the diagnostic model more robust and fair, and avoiding arbitrary conclusions due to incomplete data.

[0038] Its function is to normalize all possible "suspects"; This indicates that the prerequisite knowledge points for all candidates are accumulated. Summation range: Represents the current incorrect knowledge point The set of all directly relevant prerequisite knowledge points; if the error is "unable to solve a quadratic equation," then... This may include "factorization", "completing the square", "quadratic formula", etc.

[0039] The "original suspicion scores" of all candidate knowledge points are summed up, and the result is used as a benchmark for the final... The values ​​will be compressed into the range [0, 1], which makes... It has interpretability in a probabilistic sense, that is, "among all possible causes, What is the probability that it is the root cause?

[0040] Specific calculation example To demonstrate the application of this formula more intuitively, we construct a specific teaching scenario; Scenario: When a student was solving the equation (x-1)(x-2)=0, he only wrote x=1 and omitted x=2; System diagnostic process: Error identification: The system identified an error in step x=1; Error Classification: The error type is classified as "incomplete solution set".

[0041] Related knowledge points: The knowledge points directly related to this error It means "solving quadratic equations in one variable using factorization".

[0042] Searching for prerequisite knowledge points: The system searches within the Mathematical Knowledge Graph Database 105. The direct prerequisite knowledge points are used to obtain the set. = {"Factorization", "The concept of roots of an equation"}; Retrieving Historical Data: The system queried user profile database 106 and found that the student's historical records were as follows: I did 20 factorization problems, and got 2 wrong. (Factorization) = 2 / 20 = 0.1; Regarding the concept of "roots of an equation," I did 15 questions and got 6 wrong. (The concept of roots of an equation) = 6 / 15 = 0.4.

[0043] Setting parameters: System preset smoothing factor =0.5; Calculate the degree of suspicion: For "factorization": = (Factorization)+ =0.1 + 0.5 = 0.6 Regarding the concept of "the roots of an equation": = (The concept of roots of an equation) + =0.4 + 0.5 = 0.9 calculate (Total Score): =(0.1 + 0.5)+(0.4 + 0.5)=0.6+0.9=1.5 Calculate the final suspicion level : Factorize 0.6 / 1.5 = 0.4 (The concept of roots of an equation) = 0.9 / 1.5 = 0.6 Diagnostic findings and teaching interventions: The system compared the two suspicion levels, and 0.6 > 0.4. Therefore, it determined that the "concept of the roots of the equation" was the root cause of this error. Subsequently, the generative teaching module 104 will not repeatedly explain the techniques of factorization, but will call on generative AI to generate heuristic teaching content on the "concept of the roots of an equation". For example, it will use the analogy of "switching circuit" or "balanced scale" to explain the principle of "why at least one factor is zero when the product is zero", thereby accurately making up for the students' cognitive shortcomings.

[0044] In this embodiment, specifically, refer to... Figure 1This embodiment provides a teaching system for mathematical problems and solutions. The system includes a user interaction module 101, a problem analysis and standardization module 102, a cognitive diagnostic engine 103, a generative teaching module 104, a mathematical knowledge graph database 105, and a user profile database 106. User interaction module 101 is the front-end interface for information exchange between the system and the user. Its input end supports multiple modalities: users can input text and LaTeX formulas via keyboard, input handwritten formulas via touch screen or handwriting tablet (the module has built-in OCR technology for recognition), input voice via microphone (the module has built-in ASR technology for transcription), or take pictures of paper questions via camera (the module has built-in image recognition and OCR technology). Its output end also supports multiple modalities: it can not only display text and static images, but also render dynamic geometric transformation animations using WebGL and other technologies, and play voice explanations through TTS technology. The question parsing and standardization module 102 is the system's understanding center. When it receives a question input by the user, this module uses natural language processing (NLP) technology to understand the question and uses a symbolic computing engine (such as SymPy) to convert it into machine-readable structured data. The question "Solve the equation x²-5x+6=0" will be parsed as {type:"quadratic_equation",variable:"x",coefficients:[1,-5, 6]}. At the same time, this module will query the mathematical knowledge graph database 105 to obtain one or more standard solution paths associated with the question type. The Cognitive Diagnostic Engine 103 is used for in-depth analysis of users' thought processes. Solution Path Comparison Unit 1031 assumes the user inputs the following sequence of solution steps: Step 1: x²-5x+6=0, Step 2: (x-2)(x-3)=0, Step 3: x=2; one standard path is Std_Step1: x²-5x+6=0, Std_Step2: (x-2)(x-3)=0, Std_Step3: x-2=0 or x-3=0, Std_Step4: x=2 or x=3. Solution Path Comparison Unit 1031 will use... By performing a layer-by-layer comparison, it will find that the user's Step3 is significantly different from the standard Std_Step3 and Std_Step4, and therefore Step3 will be marked as the difference step node; The error classification unit 1032 has a built-in error type knowledge base. Based on the phenomenon of "missing a solution", it will query the knowledge base and classify it as "incomplete solution set" under the "logical error" subclass. Knowledge Graph Tracing Unit 1033 Reference Figure 2The knowledge point directly related to this error is "finding the roots of a quadratic equation in one variable," which will be covered in the knowledge graph of this unit. In the process, it searches for all preceding nodes of the "finding roots of a quadratic equation" node, namely "factorization" and "the concept of roots of an equation". Then it queries the user profile database 106 to find the user's historical error frequency on the "the concept of roots of an equation" node. The suspicion level is very high. Calculated using the "suspicion level" formula, the "concept of the roots of the equation" has the highest suspicion level, therefore it is positioned as the root cause knowledge point. Generative teaching module 104 is responsible for implementing personalized teaching. This module receives the following diagnostic results: Error_Type: "Incomplete solution set", Root_Concept: "The concept of the root of the equation"; It retrieves the student's Student_Profile from user profile database 106: {learning_style:"visual",grade:"Junior High Eighth Grade"}; Based on the preset teaching strategy library, the system selected the Teaching_Strategy which combines "Socratic questioning" and "visual demonstration". The module then constructed the following teaching instruction (Prompt): "A junior high school student, when solving the equation (x-2)(x-3)=0, only got x=2; His learning style is visual; he clearly doesn't understand the principle that 'if AB=0, then A=0 or B=0': 1. Explain the principle using an analogy of a balance scale or a switching circuit; 2. Ask a guiding question so he can think for himself about why x=3 is also a solution.

[0045] When this prompt is fed into a pre-trained large language model (such as GPT-4), the model will generate heuristics such as: "Imagine that (x-2) and (x-3) are two switches connected in series, and the light bulb will only light up when both switches are closed." The light bulb is currently off (the product is 0). What does this mean? Does it mean that at least one switch is off? Besides the switch x-2 (x=2) being off, is it possible that another switch is off? Mathematical Knowledge Graph Database 105 Figure 2 As shown, this is a large directed graph; node Representing mathematical concepts such as "function", "derivative", and "set", and side It represents the logical relationship between knowledge points, such as "is_prerequisite_of", "contains", and "applies_to". Each node also has additional attributes, such as knowledge point description, typical examples, and common error pattern IDs. The user profile database 106 records each student's long-term learning data. The level of knowledge mastery can be dynamically quantified and updated using a Bayesian Knowledge Trace (BKT) model or a Deep Knowledge Trace (DKT) model. Learning preference tags can be obtained through user behavior analysis or questionnaires.

[0046] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A teaching system for mathematical problems and solutions, characterized in that, It includes a user interaction module, a question analysis and standardization module, a cognitive diagnostic engine, a generative teaching module, a mathematical knowledge graph database, and a user profile database. The user interaction module is used to receive mathematical problems and solutions input by the user, and to present teaching content and guiding questions to the user in a multimodal format. The problem parsing and standardization module is used to perform semantic understanding and structured parsing of mathematical problems, and generate standardized problem descriptions and at least one standard solution path. The cognitive diagnostic engine is communicatively connected to the question parsing and standardization module. The cognitive diagnostic engine includes a problem-solving path comparison unit, an error classification unit, and a knowledge graph tracing unit. The problem-solving path comparison unit is used to compare the user's problem-solving process sequence with the standard problem-solving path sequence layer by layer, and identify the steps and nodes that differ from each other. The error classification unit is used to label the different step nodes with error types based on a preset error type knowledge base. The error types include at least conceptual errors, calculation errors, and logical errors. The knowledge graph tracing unit is used to trace back along the dependency edges in a pre-built mathematical knowledge graph based on the knowledge points associated with the different step nodes, in order to locate at least one root cause knowledge point that caused the error. The generative teaching module is communicatively connected to the cognitive diagnostic engine, the mathematical knowledge graph database, and the user profile database. The generative teaching module is used to receive the error type and root cause knowledge points output by the cognitive diagnostic engine, and to retrieve the user's historical learning data from the user profile database. Based on error type, root cause knowledge points, and user's historical learning data, a dynamic teaching instruction is constructed. Input teaching instructions into a pre-trained generative AI model to generate personalized, heuristic teaching content; The mathematical knowledge graph database stores structured mathematical knowledge points, prerequisite relationships between knowledge points, and common error patterns associated with each knowledge point. The user profile database stores a user's problem-solving history, error records, quantitative values ​​of their mastery of knowledge points, and learning preference tags.

2. The teaching system for mathematical problems and solutions according to claim 1, characterized in that, The user interaction module supports at least one of the following multimodal inputs: text input, handwritten formula recognition, voice input, and image question recognition; the multimodal outputs include at least one of the following: text, graphics, animation, and voice.

3. The teaching system for mathematical problems and solutions according to claim 1, characterized in that: The problem-solving path comparison unit uses a sequence matching-based algorithm to calculate the similarity between the user's problem-solving steps and the standard problem-solving steps. When the similarity is lower than a preset threshold, the step is marked as a difference step node.

4. The teaching system for mathematical problems and solutions according to claim 1, characterized in that, The teaching instructions constructed by the generative teaching module follow the following logical function: Prompt=f(Error_Type,Root_Concept,Student_Profile,Teaching_Strategy) Among them, Prompt is the generated teaching instruction, Error_Type is the error type, Root_Concept is the root cause knowledge point, Student_Profile is the user profile, and Teaching_Strategy is the teaching strategy selected from the preset strategy library. The teaching strategies include Socratic questioning, analogical explanation or visual demonstration.

5. The teaching system for mathematical problems and solutions according to claim 4, characterized in that: When the Teaching_Strategy is a Socratic question, the teaching content generated by the generative teaching module includes one or more guiding questions. These questions are designed to create a cognitive conflict scenario to encourage users to discover and correct their own erroneous logic.

6. A method for teaching mathematical problems and solutions, characterized in that, Includes the following steps: S1. Receive math problems and corresponding solutions submitted by users through the user interaction module; S2. Using the problem analysis and standardization module, the mathematical problem is analyzed, and the core knowledge points associated with the problem and at least one standard solution path are extracted from the mathematical knowledge graph database. S3. Through the cognitive diagnostic engine, the user's problem-solving process is compared with the standard problem-solving path to identify the erroneous steps that differ from the standard. S4. Classify the identified erroneous steps by error type and use mathematical knowledge graphs to trace the root cause knowledge points that led to the error; S5. Combining the error types, root cause knowledge points, and user historical learning data retrieved from the user profile database, construct a personalized teaching instruction. S6. Input the teaching instructions into the generative AI model to generate heuristic teaching content; S7. Through the user interaction module, the generated teaching content is presented to the user, and user feedback is received. The user profile in the user profile database is updated based on the feedback.

7. The method for teaching mathematical problems and solutions according to claim 6, characterized in that: In step S3, the user steps are calculated using the following algorithm formula. With standard procedures similarity : in, and Operators representing user steps and standard steps, respectively. and Represents operands, and These are the similarity functions for operators and operands, respectively. and These are preset weighting coefficients, and When similarity Below a preset threshold If this happens, the step is determined to be an erroneous step.

8. The method for teaching mathematical problems and solutions according to claim 6, characterized in that: In step S4, the knowledge graph tracing process includes starting from the knowledge point node corresponding to the erroneous step. Let's start with knowledge graphs. Search for all its directly preceding knowledge point nodes in the middle. And based on the historical error frequency in the user profile database, calculate each prerequisite knowledge point. "Suspicion" : in, It is the user's prior knowledge points Historical error frequency It is a smoothing factor used to avoid zero-frequency problems; Select "Suspicion Level" The most important prerequisite knowledge point is the fundamental reason knowledge point.

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