Multi-scale mathematical modeling method and system for artificial intelligence teaching

Abstract

The invention relates to the technical field of intelligent education, in particular to a multi-scale mathematical modeling method and system for artificial intelligence teaching, and the method comprises the steps: receiving a mathematical problem description text of a user and a historical modeling error question record, and carrying out the standardization processing to generate a data set; generating a bottleneck distribution matrix and a knowledge point weak topological graph by analyzing the characteristics of wrong questions in the links of model conception and definition, construction and implementation, and solving and verification; deconstructing a problem semantic generation element list, and dynamically generating an integrated mathematical model containing guide content in combination with a bottleneck matrix; and finally, based on the core knowledge point codes and the topological graph, planning, remedying, consolidating and expanding three-level learning paths, and fusing the model to generate a knowledge development report. According to the method, precise diagnosis of weak links, personalized guidance and closed-loop support of system learning planning are realized, and the pertinence and systematicness of mathematical modeling learning are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent education technology, in particular to a multi-scale mathematical modeling method and system for artificial intelligence teaching. BACKGROUND

[0002] Mathematical modeling is the core ability of abstracting and transforming real problems into mathematical problems and solving them, and is the key link to cultivate students' logical thinking and innovation ability. Current artificial intelligence technology has been integrated into the teaching field to provide personalized learning support, but in the teaching of mathematical modeling, a complex cognitive process, the existing technology has obvious limitations:

[0003] First, the existing technology lacks accuracy in bottleneck positioning; mathematical modeling is a multi-link progressive process including model conception and definition, construction and implementation, solution and verification, and students' errors often focus on the knowledge gap or method defect of a specific link. But the existing technology mostly focuses on right or wrong judgment at the knowledge point level, lacks deep mining of the distribution characteristics of error data in the whole modeling process, and cannot accurately locate the core bottleneck of students in specific modeling links, resulting in superficial diagnostic results and failing to provide accurate basis for personalized intervention.

[0004] Second, the existing technology lacks analysis of weak structures of knowledge points; the mathematical knowledge system has strict logical correlation, and the weakness of a single knowledge point often leads to a chain of learning obstacles, while the existing technology mostly analyzes the mastery of a single knowledge point in isolation, without building the association topology relationship between knowledge points, and cannot reveal the pre-requisite dependency, horizontal association and downstream influence of weak points, resulting in a lack of systematicness in learning intervention and difficulty in filling knowledge structure gaps from the root.

[0005] Third, the existing technology is out of touch with the needs of individualized modeling guidance; existing automated modeling assistance tools mostly provide general step-by-step guidance or model templates, without dynamically integrating students' individualized weak diagnosis results with the modeling process. The bottlenecks encountered by students in the modeling process are often directly related to their knowledge gaps, and general guidance cannot solve the individual's confusion in specific links, causing a disconnect between modeling support and actual learning needs and making it difficult to effectively improve students' modeling ability.

[0006] Finally, the learning path planning of the existing technology lacks multi-scale adaptability; the learning path generated by the existing technology is mostly a single-dimensional list of knowledge points, without considering the students' weak degree, the logical level of knowledge points and the advanced needs of modeling ability to divide differentiated learning levels. This makes the learning path either limited to basic remediation or blindly expanded, failing to achieve the goal of systematic improvement.

[0007] In summary, the prior art is difficult to provide precise, systematic and personalized teaching support that matches the complex cognitive process of mathematical modeling, which restricts the improvement of mathematical modeling teaching quality and the cultivation of students' core competence, and reduces the teaching efficiency. SUMMARY

[0008] To this end, the technical problem to be solved by the present application is to overcome the problem that the prior art cannot realize precise and personalized teaching support, resulting in poor teaching quality and low efficiency.

[0009] To solve the above technical problems, the present application provides a multi-scale mathematical modeling method for artificial intelligence teaching, comprising: preprocessing the user input mathematical description text to obtain a standard mathematical problem text; Converting historical mathematical error question records into structured data of a preset structure, and obtaining error step sequence numbers, error description texts, deduction values, total scores of the questions, and knowledge point identifiers to form error question samples and build an error question data set; Based on the error identifier mapping rule, obtain the modeling link identifier corresponding to each error question sample; count the error frequency of each knowledge point identifier in each modeling link, select the key bottleneck link of each knowledge point identifier, and form a bottleneck distribution matrix; Based on all knowledge point identifiers in the error question data set and the standard knowledge structure, a knowledge point association graph is constructed; the error severity of each knowledge point identifier is obtained, and combined with the knowledge point association graph, the target weakness score of each knowledge point identifier is obtained, the core weak point is identified and obtained, and a knowledge point weakness topology map is constructed; The standard mathematical problem text is converted into a word unit sequence, which is input into a mathematical semantic recognition model to extract mathematical entities and the relationship between entities, and is mapped to the corresponding semantic role category to construct a semantic element list of the standard mathematical problem text; Based on the semantic element list of the standard mathematical problem text and its associated knowledge point identifier, the core knowledge point code is obtained; the key bottleneck link corresponding to the knowledge point identifier matching the core knowledge point code in the bottleneck distribution matrix is selected to form a key bottleneck link identifier set, and the basic mathematical model framework is guided to generate a guided integrated mathematical model; Correlation analysis of the core knowledge point code of the standard mathematical problem text and the knowledge point weakness topology map generates a multi-scale extended learning path, which is combined with the guided integrated mathematical model to obtain a user's mathematical modeling knowledge development report.

[0010] The above technical solutions of the present application have the following beneficial effects compared with the prior art: The multi-scale mathematical modeling method for artificial intelligence teaching provided by the application, based on historical error question data, splits three links of model conception and definition, model construction and implementation, model solving and verification, generates a bottleneck distribution matrix through an error frequency and self-adaptive threshold algorithm, and accurately locks the weak points of knowledge points in specific modeling links; at the same time, the weak degree score is calculated by fusing the error frequency, error severity and knowledge point correlation, a knowledge point weak topology graph is constructed, the depth analysis from single point weakness to knowledge structure short board is realized, and the problems of scattered diagnosis and lack of systematization in the prior art are solved.

[0011] Based on the core elements of the question extracted by semantic analysis, the application dynamically embeds adaptive guide content in the basic mathematical model framework in combination with the bottleneck diagnosis result, provides targeted guidance such as target function analysis, constraint condition derivation and algorithm step decomposition for different bottleneck links, strongly binds the guide content with the weak points of students, avoids generalization assistance, realizes real-time echo of modeling steps and individual short board, and solves the defects of disconnection between modeling support and knowledge short board in the prior art.

[0012] The application takes the core knowledge point coding as a starting point, divides three learning levels of remediation, consolidation and expansion according to the weak degree score and the topology chain type, forms a ladder type path from completing the preposition basis, strengthening the current core to extending the downstream knowledge, deeply fuses the learning path with the guide model and the diagnosis result, generates a structured knowledge development report, realizes the whole process support of finding problems, immediate guidance and long-term improvement, makes the mathematical modeling learning from fragmentation to systematization, provides reliable technical support for individualized support, and significantly improves the efficiency and quality of teaching support. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to make the content of the application more easily understood, the application will be further described in detail below according to specific embodiments of the application and in combination with the drawings, in which: Figure 1 is a step flow chart of the multi-scale mathematical modeling method for artificial intelligence teaching of the application; Figure 2 is a principle flow chart for constructing a bottleneck distribution matrix of a modeling link; Figure 3 is a knowledge point weak topology graph construction flow chart; Figure 4 is a principle flow chart for generating a guide integrated mathematical model; Figure 5 is a principle flow chart for obtaining a mathematical modeling knowledge development report; Figure 6 is a structural schematic diagram of the multi-scale mathematical modeling system for artificial intelligence teaching. DETAILED DESCRIPTION

[0014] The application will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the application and implement it, but the embodiments are not as a limitation of the application.

[0015] Referring to Figure 1 The step flow chart of the multi-scale mathematical modeling method for artificial intelligence teaching of the application is shown in FIG. 1, and the specific implementation process is shown in steps S101 to S110.

[0016] S101: Preprocess the user input mathematical description text to obtain a standard mathematical problem text, including: Perform character-level cleaning on the user input mathematical description text, identify and remove irrelevant symbols and marks, and obtain the cleaned text; Based on the general specification of mathematical language, convert the mathematical terms, symbols and expressions in the cleaned text into standard symbols and standard terms to obtain the converted text; Based on the standard mathematical grammar rules, restructure and unify the operation order, function representation, bracket level and formula layout of the converted text to obtain the standard mathematical problem text.

[0017] Specifically, first, perform character-level cleaning on the user input mathematical problem description text, traverse each character of the mathematical problem description text, identify and remove irrelevant symbols and format characters in the text, irrelevant symbols include special symbols and marks that are not required for mathematical expression, and format characters include redundant spaces, line breaks and tab characters, and after removal, obtain the cleaned text. Identify the mathematical terms, symbols and expressions in the cleaned text, convert them to standard symbol representation and unified terms according to the general specification of mathematical language by analyzing their mathematical semantics and context; then, perform syntax analysis on the mathematical expression after symbol conversion, restructure and unify the operation order, function representation, bracket level and formula layout according to the standard mathematical grammar rules; finally, output the standard mathematical problem text that meets the unified mathematical expression specification.

[0018] S102: Convert the historical mathematical mistake records into structured data of a preset structure, and obtain the error step sequence number, error description text, deduction value, total score of the question, and knowledge point identifier, to form a mistake sample and build a mistake data set.

[0019] Specifically, from the user history wrong question record data table, the history mathematical modeling wrong question record entries associated with the user identifier are read, each record entry is pre-structured data, the record entry field includes original question content, question total score, user wrong answer, error step position information marked by the system or the teacher in advance and corresponding deduction value, core knowledge point code marked in advance according to question content; for each read record, the step position and error description are extracted from the error step position information field as the error position data of the record, the error position data is a composite data item including step sequence number and error description text, wherein the step sequence number is used to identify the sequential position of the error in the standard problem solving process, and the error description text is used to record the specific content and characteristics of the error; in addition, the corresponding values are directly read from the error step deduction value and question total score fields of the same record; at the same time, the marked knowledge points are directly read from the core knowledge point code field as the knowledge point identifier associated with the record; the extracted error position data, error step deduction value, question total score, knowledge point identifier and wrong question timestamp are associated and integrated to form a structured wrong question analysis data; all processed wrong question analysis data are collected to generate a wrong question data set based on history mathematical modeling.

[0020] S103: Obtain the modeling link identifier corresponding to each wrong question sample based on the error identifier mapping rule.

[0021] Specifically, the embodiment maps the error position data in the historical mathematical modeling wrong question data set to one of the three core mathematical modeling links of model conception and definition, model construction and implementation, model solving and verification according to the error identifier mapping rule, and synchronously extracts the knowledge point identifier associated with the historical mathematical modeling wrong question.

[0022] Specifically, the embodiment constructs an error identifier link mapping classifier for modeling link identification, including: Iterate through each wrong question analysis data in the historical mathematical modeling wrong question data set, for each wrong question analysis data, extract the composite data item recorded in the error position data field, the composite data item includes step sequence number and error description text; Take the error description text as input, input the error identifier link mapping classifier constructed based on the knowledge in the field of mathematical modeling, the construction basis of the error identifier link mapping classifier is the division of core mathematical modeling links and the corresponding relationship between typical error patterns under each core mathematical modeling link; the construction process first analyzes the error description text in the historical wrong question data set, extracts high-frequency keywords, high-frequency error phrases and context co-occurrence patterns, induces typical error patterns of each core mathematical modeling link, and forms a priori rule library; On this basis, a supervised learning method is adopted, taking error description text as input, and learning the corresponding relationship between error patterns and core mathematical modeling links as the goal, to train a text classification model. The text classification model optimizes parameters through gradient descent algorithm, and learns deeper semantic and syntactic features in error description text; Finally, the prior rule library of statistical induction and the trained text classification model are combined to construct an error identification link mapping classifier that can accurately map error descriptions according to explicit features and implicit semantic patterns of text.

[0023] Among them, the error identification link mapping classifier determines the relative position of the semantic of the error description text and the step sequence number, and executes the following mapping rules: When the semantic of the error description text is clear, it is directly mapped according to the semantic: if the semantic of the error description text involves problem mathematical abstraction, key variable definition or target hypothesis, it is classified into the model conception and definition link; if the semantic of the error description text involves establishing equations, inequalities or function relationships, it is classified into the model construction and implementation link; if the semantic of the error description text involves numerical calculation, algorithm execution, result verification or error analysis, it is classified into the model solution and verification link; When the semantic of the error description text is ambiguous, the relative position of the step sequence number of the error occurrence position is determined: the steps in the first 1 / 3 interval are preferentially classified into the model conception and definition link; the steps in the middle 1 / 3 interval are preferentially classified into the model construction and implementation link; the steps in the last 1 / 3 interval are preferentially classified into the model solution and verification link.

[0024] This embodiment reads the knowledge point identifier associated with the error question from the knowledge point identifier field in the same error question analysis data while completing the mapping; combines the step sequence number, error description text, core mathematical modeling link identifier obtained by mapping, and knowledge point identifier to generate a complete error question link analysis record.

[0025] S104: Statistics of error frequency of each knowledge point identifier in each modeling link, selection of key bottleneck link of each knowledge point identifier, and composition of bottleneck distribution matrix.

[0026] Referring to Figure 2 As shown in the principle flowchart for constructing the bottleneck distribution matrix of the modeling link; specifically, this embodiment calculates the error frequency of the knowledge point identifier in each core mathematical modeling link; dynamically determines the key bottleneck link corresponding to the knowledge point identifier according to the error frequency distribution of each core mathematical modeling link and the adaptive threshold rule; integrates the key bottleneck links of all knowledge point identifiers to generate the bottleneck distribution matrix of the modeling link.

[0027] In the embodiment, all wrong question link analysis records are aggregated, and for each knowledge point identifier appearing in historical data, all wrong question link analysis records containing the knowledge point identifier are screened out. In the screened record set, the number of times that the knowledge point identifier appears in the three core mathematical modeling links of model conception and definition, model construction and implementation, and model solution and verification is counted respectively, and the error frequency of the knowledge point identifier in each core mathematical modeling link is calculated based on this. The specific calculation method is as follows: The number of times that the knowledge point identifier appears in a core mathematical modeling link is divided by the sum of the number of times that it appears in all three core mathematical modeling links, and the error frequency value of the knowledge point identifier in the core mathematical modeling link is obtained. The sum of the error frequency values of the three core mathematical modeling links is 1. For the knowledge point identifier, a distribution vector is formed based on the error frequency values of the three core mathematical modeling links , and an adaptive threshold algorithm is used to dynamically calculate a link threshold. The core function of the algorithm is as follows: ; Wherein, is the dynamically calculated link threshold, which is used to determine the weak link. represents the arithmetic mean of the distribution vector , and the physical meaning is the overall average level of the error frequency of the knowledge point identifier. represents the standard deviation of the distribution vector , and the physical meaning is the dispersion degree of the error frequency of the knowledge point in the three links. The value of the distribution sensitivity coefficient is determined based on the error frequency distribution characteristics of all knowledge points in the historical data. After the link threshold is calculated, the link with an error frequency value higher than the link threshold is marked as the key bottleneck link corresponding to the knowledge point identifier. After traversing all knowledge point identifiers and completing the above determination, all results are integrated to generate a modeling link bottleneck distribution matrix. The rows of the matrix correspond to the three core mathematical modeling links of model conception and definition, model construction and implementation, and model solution and verification, and the columns correspond to all appearing knowledge point identifiers. The matrix element value is a binary identifier: if the link corresponding to a certain row is determined as the key bottleneck link of the knowledge point corresponding to the column, the corresponding matrix element value is 1, otherwise it is 0.

[0028] Wherein, the distribution sensitivity coefficient The specific process is: calculating the standard deviation of the error frequency distribution of each knowledge point in the historical data, and calculating the average and median of the standard deviations; taking the average of the obtained average and median, a reference value reflecting the dispersion degree of the overall distribution is obtained; dividing the preset constant by the reference value, the value of the coefficient a is obtained. In this embodiment, the default preset constant is 0.15, which corresponds to a confidence level of about 85%, which is an empirical sensitivity factor that matches the significant but not harsh judgment standard; the calculation method aims to adaptively adjust the link threshold according to the general level of data dispersion, so as to keep the sensitivity of the threshold judgment consistent in the whole system.

[0029] S105: Based on all knowledge point identifiers in the error question data set and the standard knowledge structure, a knowledge point association graph is constructed; the error severity of each knowledge point identifier is obtained, and the target weakness score of each knowledge point identifier is obtained by combining the knowledge point association graph, the core weak points are identified and obtained, and a knowledge point weakness topology graph is constructed, including: S105-1: All knowledge point identifiers in the error question data set after deduplication are taken as nodes; the association relationship between the knowledge point identifiers is obtained based on the standard knowledge structure, and the connection edges are constructed; based on all nodes and connection edges, a knowledge point association graph is formed; S105-2: The ratio of the deduction value of each error question sample to the total score of the question is taken as the error score of each error question sample; the error scores of each error question sample belonging to the same knowledge point identifier are arithmetically averaged to obtain the error severity of each knowledge point identifier; S105-3: Based on the knowledge point association graph, an iterative updating algorithm is used to calculate the weakness score of each node after a preset number of iterations, which is taken as the target weakness score of the knowledge point identifier represented by each node; S105-4: The sum of the average and standard deviation of the target weakness scores of all nodes is taken as the weakness threshold; the nodes with a target weakness score greater than the weakness threshold are taken as the core weak points; S105-5: For each core weak point, in the knowledge point association graph, the prerequisite knowledge chain, the flat knowledge point set and the downstream influence chain of each core weak point are obtained to form a knowledge point weakness topology graph; Among them, the predecessor nodes directly or indirectly connected with the core weak point are recursively traversed along the in-degree direction of the core weak point to form the prerequisite knowledge chain; the nodes connected with the core weak point through undirected edges form the flat knowledge point set; the successor nodes directly or indirectly connected with the core weak point are recursively traversed along the out-degree direction of the core weak point to form the downstream influence chain.

[0030] Reference Figure 3The diagram shown is a flowchart for constructing a topology graph of weak knowledge points. Specifically, in this embodiment, the incorrect question dataset from historical mathematical modeling is analyzed, and all unique knowledge point identifiers are extracted as nodes in the knowledge point association graph. Based on the knowledge structure of the mathematics teaching system, the association relationships between knowledge point identifier nodes are defined and directed edges are formed, divided into three categories: strong dependency, general association, and weak reference. Strong dependency refers to the establishment of a directed edge from A to B when knowledge point A is a direct prerequisite for knowledge point B (i.e., mastering A is a prerequisite for learning B). The identification basis is the strict sequence and definition reference relationship between knowledge points in the curriculum standards and textbooks, so it is given the highest weight value in this embodiment. General association refers to establishing a bidirectional undirected edge when knowledge point A and knowledge point B often appear side by side or in contrast in teaching; it is identified by statistically analyzing the stable co-occurrence frequency between knowledge points in a large number of exercises, lesson plans and test papers, and is assigned a medium weight accordingly. A weak reference relationship refers to a directed edge established from A to B when knowledge point A only serves as background or extended reference for understanding knowledge point B. The identification of weak reference relationships is based on contextual hints and supplementary explanations in teaching materials, and therefore, in this embodiment, it is set to the lowest value among the three types of association weights.

[0031] In this embodiment, the weight allocation of association relationships is differentiated based on the cognitive dependence strength of different relationship types, and the specific normalized values ​​are stored in the teaching logic relationship mapping table. When constructing the knowledge point association graph, the corresponding weight in the teaching logic relationship mapping table is called according to the edge type to complete the assignment, and finally the knowledge point association graph is generated. In this embodiment, the default weight of strong dependency relationship is 0.7, the weight of general association relationship is 0.4, and the weight of weak reference relationship is 0.1.

[0032] Specifically, for each knowledge point identifier node, the severity of its error is calculated: all error analysis data related to that knowledge point identifier are selected from the historical mathematical modeling error dataset; for each data point, the error score for a single question is calculated by dividing the deduction value for the erroneous steps by the total score of the question. For all related incorrect questions Calculate the arithmetic mean to obtain the error severity of the node identifying the knowledge point. .

[0033] Specifically, based on the knowledge point association graph, an iterative update algorithm is used to calculate the weakness score of each knowledge point identifier node in the graph. The core function of the algorithm is as follows: For knowledge point identification nodes , its first Weakness score in the next iteration The calculation is as follows: ; wherein, is the knowledge point identification node corresponding to the knowledge point identification node is the knowledge point identification node corresponding to the knowledge point identification node represents a set of all neighbor knowledge point identification nodes directly connected to the knowledge point identification node in the knowledge point association graph; is the edge connecting the knowledge point identification node and the neighbor knowledge point identification node , the weight of the edge is , the value of which is obtained by querying the corresponding preset weight from the teaching logic relationship mapping table according to the association relationship type represented by the edge; is the neighbor knowledge point identification node , the weakness score of which at the first iteration is ; is the weighted average weakness of the current knowledge point affected by all directly associated knowledge points, which is obtained by calculating the weighted average value of the weakness scores of all neighbor knowledge point identification nodes directly connected to the current knowledge point identification node ; is the influence level of the neighbor knowledge point identification node on the current knowledge point identification node, which is obtained by calculating the weighted average value of the weakness scores of all neighbor knowledge point identification nodes directly connected to the current knowledge point identification node and are weight coefficients, used to balance the contribution proportion of the properties of the knowledge point identification node (error frequency, error severity) and the influence of its neighbor knowledge point identification nodes in the weakness calculation, the specific values of which are determined by grid search method on historical mathematical modeling mistake data set: all parameter combinations within the solution space are traversed, and the Gini coefficient of the weakness score distribution of all knowledge points under each parameter combination is calculated; finally, the parameter combination that minimizes the Gini coefficient is selected as the final value of and to achieve the optimal discrimination degree of the score distribution; in this embodiment, by default and are both within the interval [0.1, 0.4] with a step size of 0.05, and satisfy .

[0034] In this embodiment, at the initialization of iteration, the of all knowledge point identification nodes is set to 0; the termination condition of iteration is that the absolute value of the score change of all knowledge point identification nodes before and after two iterations is less than a preset convergence threshold , i.e. satisfies ; the threshold is set according to the calculation accuracy requirement, and is usually valued at to​ between the two, in the embodiment to ensure the stability of the vulnerability score with centile precision, while avoiding unnecessary iterative calculations. The final target vulnerability score obtained after the iteration is terminated is the knowledge point identification node the final target vulnerability score.

[0035] Specifically, the embodiment identifies the core weak point according to the knowledge point association graph and the vulnerability score of each knowledge point identification, and traces the front, flat and subsequent knowledge point identifications of the core weak point in the knowledge point association graph to generate a knowledge point weak topology graph containing complete topological relationships.

[0036] Among them, based on the constructed knowledge point association graph and the vulnerability score of each knowledge point identification node, the core weak point is identified, including: calculating the average value of the target vulnerability score of all knowledge point identification nodes and the standard deviation , the core vulnerability threshold is set to ; traverse all knowledge point identification nodes in the knowledge point association graph, and mark the knowledge point identification nodes with vulnerability score greater than the core vulnerability threshold as core weak points.

[0037] Among them, for each identified core weak point, topological relationship tracing is performed in the knowledge point association graph, including: recursive traversal along the in-degree direction (i.e. all directed edges pointing to the core weak point), accessing all direct or indirect front knowledge point identification nodes, forming the front knowledge chain of the core weak point; find all knowledge point identification nodes directly connected to the core weak point through undirected edges (i.e. general association relationship edges) in the knowledge point association graph, forming the flat knowledge point set of the core weak point; recursive traversal along the out-degree direction (i.e. all directed edges pointed out by the core weak point), accessing all direct or indirect successor knowledge point identification nodes, forming the downstream influence chain of the core weak point.

[0038] Among them, the core weak point and all knowledge point identification nodes and association relationships (including node attributes and relationship type and weight of edges) in the front knowledge chain, flat knowledge point set and downstream influence chain corresponding to the core weak point are integrated and encapsulated to generate a knowledge point weak topology graph containing complete topological structure, attribute information and association relationship.

[0039] S106: Convert the standard mathematical problem text into a sequence of lexical units, input the mathematical semantic recognition model, extract mathematical entities and entity relationships, and map them to corresponding semantic role categories to construct a semantic element list of the standard mathematical problem text. ​

[0040] Specifically, the multi-granularity word segmentation processing of the embodiment calls a preset mathematical field word segmentation dictionary, performs a bidirectional scanning matching word segmentation algorithm on the input standard mathematical problem text, determines a final segmentation scheme, and converts the continuous standard mathematical problem text into a sequentially arranged sequence of vocabulary units with independent mathematical semantics.

[0041] The construction process of the mathematical field word segmentation dictionary is specifically as follows: professional terms, mathematical symbols, and compound expressions in mathematical teaching materials, mathematical academic literature, and standardized test syllabuses are systematically collected and integrated to form a basic term set; then, according to the normative definition of mathematical grammar and semantics, a structured analysis process is used to label the mathematical part-of-speech category and word formation boundary features of each term, wherein the word formation boundary features are used to identify the rules for cutting the term as an independent semantic unit in continuous text; finally, all the labeled terms and attribute information are structured and stored to form a mathematical field word segmentation dictionary serving the word segmentation function.

[0042] The bidirectional scanning matching word segmentation algorithm includes the following steps: first, perform forward scanning, start from the starting character of the standard mathematical problem text, and match the mathematical field word segmentation dictionary term with the maximum length, sequentially determine all forward segmentation points, and generate a candidate vocabulary unit sequence. Then, perform reverse scanning, start from the ending character of the standard mathematical problem text, and proceed forward with the same maximum length matching principle to generate another candidate vocabulary unit sequence. Then, compare the two candidate vocabulary unit sequences obtained by forward and reverse scanning, and determine the final unique sequence according to the preset disambiguation rule; the disambiguation rule is: preferentially select the candidate vocabulary unit sequence with fewer total number of segmented vocabulary units; if the total number of units of the two candidate vocabulary unit sequences is the same, preferentially select the candidate vocabulary unit sequence that cuts the compound mathematical expression as a whole.

[0043] Specifically, the embodiment inputs the vocabulary unit sequence into a pre-trained mathematical semantic recognition model, recognizes and extracts mathematical entities therefrom, analyzes the mutual relationships between the mathematical entities, and generates a mathematical entity and relationship set.

[0044] The pre-trained mathematical semantic recognition model is based on an encoder multi-task head architecture. The construction process first relies on structured data processing of mathematical field texts: collecting text corpus in mathematical textbooks, academic literature and historical mathematical modeling mistake sets, and performing structured labeling on mathematical elements appearing therein according to mathematical grammar and semantic specifications. The first re-labeling assigns entity category labels (including known quantities, unknown quantities, constants, and parameters) to each mathematical element, and the second re-labeling assigns relationship category labels (including equality, inequality, and function dependence) to entity pairs having logical associations. Based on this labeled corpus, the mathematical semantic recognition model uses a Transformer-based encoder to obtain deep semantic representations of the input, and connects two independent classifiers as task heads, corresponding to entity classification and relationship classification tasks, respectively. The mathematical semantic recognition model is trained through end-to-end supervised learning. The loss function of the mathematical semantic recognition model is the weighted sum of the entity classification loss and the relationship classification loss. The training goal is to minimize the difference between the model prediction and the structured labeling, so that the mathematical semantic recognition model masters the semantic pattern of joint extraction of structured knowledge from mathematical texts.

[0045] In the application stage, the mathematical semantic recognition model processes the input word unit sequence in the following process: first, input representation is performed, in which a position code is assigned to each word unit in the word unit sequence and converted into a vector through an embedding layer to form an initial sequence representation; then, the representation is input into the Transformer encoder, and through the calculation of the multi-head self-attention mechanism and the multi-layer feedforward network, a deep feature sequence containing global context information is output; then, the deep feature sequence is simultaneously fed into the two pre-trained task heads of entity classification and relationship classification: the entity classification head predicts the entity category of each word unit accordingly, and the relationship classification head analyzes the semantic association between all possible entity pairs and predicts the relationship type of the semantic association; finally, the system structures all the recognized mathematical entities and their categories, as well as the relationships between the entities and their types, and generates a mathematical entity and relationship set.

[0046] Specifically, the present embodiment maps the mathematical entity and relationship set to the corresponding semantic roles based on a classification system of four types of semantic roles: target, variable, constraint, and relationship, and performs standardized naming and coding to generate a semantic element list.

[0047] The embodiment performs mapping according to a preset mathematical semantic role classification system, which defines four types of core semantic roles and four types of core semantic role discrimination rules: if a mathematical entity or a relationship expression contains an extremum or optimization semantics, or directly points to a final solution target of a problem, the mathematical entity or the relationship expression is mapped to a target class role; if a mathematical entity is not assigned a specific numerical value in a context and the value of the mathematical entity needs to be determined by solving, or is defined as an unknown quantity to be solved, the mathematical entity is mapped to a variable class role; if a mathematical relationship is an equation or an inequality, and the function of the mathematical relationship is to limit the variable value range or define the feasible region, the mathematical relationship is mapped to a constraint class role; if a mathematical relationship is used to express the functional dependence between variables, formula association or mathematical operation relationship, and does not directly act as a constraint or target, the mathematical relationship is mapped to a relationship class role.

[0048] Traverse the set of mathematical entities and relationships, and map the mutual relationship between each mathematical entity and mathematical entity pair to the corresponding semantic role category according to the discrimination rules of the mathematical semantic role classification; after completing the mathematical semantic role classification mapping, the semantic elements that have completed the mathematical semantic role classification are standardized and organized, a unique standardized symbol is generated for each semantic element, and the semantic role category corresponding to the semantic element is recorded; finally, all semantic elements and standardized symbols of the semantic elements, semantic role information are organized into a structured record list to generate a semantic element list.

[0049] S107: Based on the semantic element list of the standard mathematical problem text and the associated knowledge point identifier, obtain the core knowledge point code; select the key bottleneck link corresponding to the knowledge point identifier matched with the core knowledge point code in the bottleneck distribution matrix to form a key bottleneck link identifier set.

[0050] In this embodiment, based on the semantic role weight of each mathematical element in the semantic element list and the hierarchical weight of the associated knowledge point, the comprehensive weight is calculated to determine the core knowledge point code corresponding to the standard mathematical problem text; the key bottleneck link identifier is extracted based on the core knowledge point code query modeling link bottleneck distribution matrix.

[0051] This embodiment parses the semantic element list, extracts the standardized symbol of the semantic element, and performs knowledge point code parsing according to the pre-constructed symbol knowledge point hierarchical mapping table. The construction of the symbol knowledge point hierarchical mapping table first extracts mathematical symbols and context description texts in which the mathematical symbols appear from the mathematical modeling course standards, teaching materials and question bank contents to form original mapping pairs; secondly, based on the mathematical field knowledge, the context description texts are semantically analyzed, the corresponding core knowledge point codes are identified and associated, and the corresponding relationship between the symbols and the knowledge points is established; according to the cognitive function and teaching positioning of the knowledge points, the knowledge point hierarchical division is implemented, and the hierarchical annotation is completed for each knowledge point code.

[0052] The specific rules for classifying knowledge points into hierarchical levels are as follows: When a knowledge point represents a clearly defined, fixed-step basic operation or fact, it is classified as the basic operation level. This type of knowledge is the basic unit of mathematical expression and calculation, and teaching focuses on memorization and direct application. When a knowledge point represents a universal mathematical idea, principle, theorem, or core method, it is classified as the core concept level. This type of knowledge is a general model for solving a class of problems, and teaching emphasizes a deep understanding of its internal logic and typical application. When a knowledge point represents the integration, modeling, and innovative application of multiple lower-level knowledge, it is classified as the comprehensive application level. This type of knowledge is geared towards complex practical problems, and teaching focuses on cross-knowledge point modeling and the cultivation of higher-order thinking. Based on this symbolic knowledge point hierarchy mapping table, this embodiment can obtain the knowledge point code corresponding to the standardized symbol and the cognitive level of the knowledge point code.

[0053] In this embodiment, the comprehensive weight of each parsed knowledge point code in this problem is calculated using the following function: ; in, The list of representative semantic elements contains all elements mapped to knowledge point codes. A set of standardized symbols for mathematical elements. It is based on symbols The fixed weight coefficients assigned to the semantic role categories within the semantic element list are used to characterize the importance of that role in encoding the core knowledge points for location. The values ​​are set by analyzing a large-scale historical problem dataset, statistically analyzing the frequency and contribution of each semantic role in successfully locating the core knowledge point encoding, and normalizing them to obtain a quantitative weight that reflects the relative importance of different roles in the localization process. It is based on knowledge point coding In a predefined knowledge system, the fixed weight coefficients set for hierarchical attributes are used to characterize the comprehensiveness and importance represented by that knowledge point level. The values ​​are set based on the allocation of teaching resources corresponding to each level in the standard teaching framework. By analyzing the curriculum standards, the proportion of three types of content—integrated application, core concepts, and basic operations—in total teaching hours, core competency items, and assessment is statistically distributed. This distribution is then normalized and mapped to the initial weights of each level. The comprehensive weight calculation function calculates the weights by accumulating the knowledge point codes. The overall weight of the knowledge point encoding is calculated by considering the contribution of each standardized symbol associated with it. The contribution of each standardized symbol is determined by its semantic role weight. and the hierarchical weight of the knowledge points A joint decision.

[0054] In this embodiment, after the calculation is completed, a comprehensive weight is selected. The highest knowledge point code is used as the core knowledge point code corresponding to the standard mathematical problem text. The core knowledge point code is precisely matched with the column header (i.e., knowledge point identifier) ​​in the bottleneck distribution matrix of the modeling process to locate the corresponding matrix column. The column vector is read, and all modeling process row identifiers marked as key bottleneck links (i.e., element value of 1) are extracted. These row identifiers represent the key bottleneck link identifiers of the core knowledge point code in the modeling process, thus forming a set of key bottleneck link identifiers.

[0055] S108: Guide the development of a basic mathematical model framework to generate a guided integrated mathematical model.

[0056] Reference Figure 4 The diagram shown is a flowchart illustrating the principle of generating a guided integrated mathematical model. Based on the semantic element list and the bottleneck distribution matrix of the modeling process, the guided integrated mathematical model is dynamically generated by identifying key bottleneck processes and dynamically embedding adaptive guidance content.

[0057] S108-1: The process for generating the basic mathematical model framework in this embodiment includes: In the model design and definition phase, semantic elements with semantic roles as target classes are extracted from the list of semantic elements, and the mathematical expression of the semantic element is formatted into a standard form of target function; at the same time, semantic elements with semantic roles as variable classes are extracted, and the standardized symbol list corresponding to the semantic element is organized into a set of decision variables. In the model building and implementation phase, semantic elements with the semantic role of constraint are extracted from the semantic element list, and the mathematical inequalities or equations of these semantic elements are arranged into a set of constraints. At the same time, semantic elements with the semantic role of relation are extracted, and the functional expressions describing the mathematical logical relationship between the variables of these semantic elements are substituted into the decision variables to construct a complete mathematical relationship between variables. In the model solving and verification stage, based on the mathematical form characteristics of the objective function and the set of constraints, a suitable mathematical optimization algorithm is determined as the model solver; if the problem is linear, a linear programming algorithm is selected; if it contains nonlinear terms, a nonlinear programming algorithm is selected; if it involves integer decision variables, an integer programming algorithm is selected. Simultaneously, corresponding model output verification indicators are set according to the problem type: for prediction or fitting problems, the root mean square error is set as the verification indicator, which is obtained by calculating the square root of the average of the sum of squares of the deviations between the predicted value and the actual value; for optimization problems, the degree to which the final obtained objective function value and all constraints are satisfied is used as a comprehensive verification indicator; thus, a basic mathematical model framework is generated, consisting of the objective function, the set of decision variables, the set of constraints, the mathematical relationships between variables, the selected solution algorithm, and the verification indicators.

[0058] S108-2: The process for generating the guided integrated mathematical model in this embodiment includes: Establish a mapping relationship between key bottleneck links and specific model components in the basic mathematical model framework. The mapping rules are as follows: if the key bottleneck link is identified as model conception and definition, then the model components that need to be enhanced are the objective function and the set of decision variables; if it is identified as model construction and implementation, then the model components that need to be enhanced are the set of constraints and the mathematical relationships between variables; if it is identified as model solving and verification, then the model components that need to be enhanced are the selected solving algorithm and verification indicators. Based on the above mapping relationship, a guided enhancement operation is performed on the basic mathematical model framework: for each key bottleneck link identifier, the model component that needs to be enhanced is located by mapping the key bottleneck link identifier, and guided content data is dynamically generated and embedded for the model component that needs to be enhanced. After completing the guidance enhancement of the model components corresponding to all key bottleneck links, the basic model components and verification indicators embedded with the guidance content are integrated and encapsulated, and the output is a guidance integrated mathematical model.

[0059] The specific rules for generating and embedding the guiding content data are as follows: For the objective function component, the generated guiding content includes a standard mathematical interpretation of the objective function and a semantic comparison with the original problem description; for the decision variable set component, the guiding content includes an explanation of the physical meaning of each variable, its definition basis, and its role in the model; for the constraint set component, the guiding content includes the step-by-step derivation process of each constraint and an explanation of the preconditions for its validity; for the mathematical relationship component between variables, the guiding content includes the source reference of the core mathematical formula, the meaning of the parameters, and the binding logic between the core mathematical formula and the decision variables; for the solution algorithm component, the guiding content includes an explanation of the basic principles of the algorithm, the reasons for its applicability to the current model form, and a breakdown of key calculation steps; for the verification index component, the guiding content includes the expansion of the index calculation formula, examples of calculation steps, and methods for interpreting the results.

[0060] S109: Correlation analysis of the core knowledge point encoding and weak knowledge point topology map of standard mathematical problem texts to generate multi-scale extended learning paths.

[0061] Specifically, based on the core knowledge point code extracted from the semantic element list, all related knowledge points that have a direct topological association with the core knowledge point code are extracted from the knowledge point weakness topology map, and the attribute information of the related knowledge points is obtained. The attribute information includes the weakness score and the type of the topology chain to which they belong.

[0062] This embodiment uses the core knowledge point code corresponding to the current problem as the query key value and performs a search in the knowledge point weakness topology graph. It retrieves all knowledge point identifier nodes that have a direct topological association with the core knowledge point code. The determination of a direct topological association includes the following two scenarios: first, direct identifier matching, meaning that in the knowledge point identifier node set of the knowledge point weakness topology graph, there exists a knowledge point identifier node whose knowledge point identifier is exactly the same as the currently queried core knowledge point code; second, graph topological connection, meaning that in the knowledge point weakness topology graph, starting from the knowledge point identifier node with direct identifier matching, all adjacent knowledge point identifier nodes connected to it by a direct edge, regardless of the direction and type of the edge, are considered to have a direct topological association with the starting knowledge point identifier node. Based on this determination, all knowledge point identifier nodes that meet the direct topological association condition are extracted as associated knowledge point identifier nodes.

[0063] For each extracted associated knowledge point identifier node, the weakness score stored in the attribute information of the associated knowledge point identifier node is read, and the topology chain type to which the associated knowledge point identifier node belongs is determined according to the graph connection relationship between the associated knowledge point identifier node and the starting node: if the associated knowledge point identifier node is upstream of the starting node (i.e., there is a directed edge from the knowledge point to the starting node), the topology chain type to which the associated knowledge point identifier node belongs is marked as a preceding knowledge chain; if the associated knowledge point identifier node is connected to the starting node through an undirected edge or a bidirectional edge, the topology chain type to which the associated knowledge point identifier node belongs is marked as a flat-layer knowledge point set; if the associated knowledge point identifier node is downstream of the starting node (i.e., there is a directed edge from the starting node to the knowledge point), the topology chain type to which the associated knowledge point identifier node belongs is marked as a downstream influence chain; finally, a list is output, in which each record contains an associated knowledge point identifier, a weakness score, and the topology chain type to which it belongs.

[0064] This embodiment starts with the encoding of core knowledge points and divides the extracted related knowledge point identifiers into three learning levels: remediation, consolidation, and expansion based on the weakness score and the topology chain type. A learning sequence is generated for the related knowledge point identifiers within each learning level, and a multi-scale extended learning path is constructed.

[0065] The learning hierarchy is divided into three parts: extracting all directly related topological knowledge point nodes of the current core knowledge point encoding, and calculating the average and standard deviation of the weakness score of each node in each of the three topological chain types: the preceding knowledge chain, the horizontal knowledge point set, and the downstream influence chain; the average value of the preceding knowledge chain is... The standard deviation of the prior knowledge chain is The average value of the knowledge point set of the flat layer is The standard deviation of the knowledge point set of the flat floor is The average value of the downstream impact chain is The standard deviation of the downstream impact chain is The current weakness score for the coding of core knowledge points is: The following adaptive threshold function is used to determine the partitioning threshold for each learning level: Remedial threshold function: ; Reinforce the threshold function: ; Extended threshold function: ; in, and The adaptive adjustment coefficient is calculated as follows: , This embodiment utilizes these two adaptive adjustment coefficients to construct a dynamic adjustment mechanism. This dynamic adjustment mechanism dynamically adjusts the threshold offset based on the dispersion of the weakness distribution within each topological chain. Specifically, when the distribution is more discrete (i.e., ... or The larger the value of the adaptive adjustment coefficient α or β, the more significant the adjustment effect (i.e., offset) on the final threshold.

[0066] Among them, the remedial threshold function By combining the current problem's weakness with the distribution characteristics of the prior knowledge chain, the system dynamically identifies significantly lagging key weaknesses as priority targets for remediation; and strengthens the threshold function. Based on the current level of weakness in the problem and the average level of knowledge mastery at the same level, similar knowledge that needs to be strengthened is selected to build a solid knowledge network; the threshold function is expanded. Based on the distribution of knowledge mastery in the downstream knowledge chain, nodes that are not mastered sufficiently and may constitute obstacles to subsequent learning are identified as learning content that can be expanded and extended.

[0067] When dividing knowledge into levels, the current core knowledge point encoding itself is unconditionally added to the reinforcement learning area; for related knowledge points in the preceding knowledge chain, if the weakness score of that related knowledge point is... satisfy If the related knowledge point is included in the remedial learning area, then the related knowledge point is included in the remedial learning area; for related knowledge points in the same knowledge point set, if the weakness score of the related knowledge point meets the requirements... If the related knowledge point is included in the consolidation learning area, then the related knowledge point is included in the consolidation learning area; for related knowledge points in the downstream influence chain, if the weakness score of the related knowledge point meets the requirements... If the related knowledge point is identified, it is included in the extended learning area. Within each learning level, the related knowledge point identifiers are sorted from high to low according to the weakness score to generate the learning sequence within that level. The three learning levels are then connected in the order of remediation, consolidation, and extension to construct a multi-scale extended learning path.

[0068] S110: Multi-scale extended learning paths combined with guided integrated mathematical models to obtain users' mathematical modeling knowledge development reports.

[0069] Reference Figure 5 The diagram shown illustrates the principle flowchart for obtaining a mathematical modeling knowledge development report. This embodiment performs correlation analysis based on the shared relationship between the multi-scale extended learning path and the guided integrated mathematical model at key bottleneck stages. Based on the correlation analysis results and the knowledge point weakness topology map, learning suggestions are generated for each related knowledge point in the multi-scale extended learning path. The multi-scale extended learning path, the guided integrated mathematical model, and the learning suggestions are encapsulated to output the mathematical modeling knowledge development report.

[0070] Specifically, the process iterates through each associated knowledge point identifier in the multi-scale extended learning path, queries the knowledge point weakness topology map for each identifier, and reads the stored weakness score and the type of topology chain to which the identifier belongs. Based on the weakness score of the associated knowledge point identifier and the logical relationship between the topology chain type to which the identifier belongs and the core knowledge point encoding, corresponding preliminary learning suggestions are generated. These preliminary learning suggestions include: first, clarifying the logical relationship between the associated knowledge point and the core knowledge point encoding; and second, qualitatively describing the mastery of the associated knowledge point based on its relative weakness score, and proposing corresponding learning guidance directions accordingly.

[0071] Simultaneously, the bottleneck distribution matrix of the modeling process is queried to locate the columns corresponding to the current core knowledge point code and the associated knowledge point identifier. The row indices with an element value of 1 in both columns are extracted to form their respective key bottleneck identifier sets. The intersection of the two sets is calculated to determine whether there are shared key bottlenecks. If the intersection is not empty, it indicates the existence of shared weaknesses. Subsequently, guidance content data corresponding to these shared weakness identifiers is extracted from the guided integrated mathematical model as a targeted strategy and added to the preliminary learning suggestions for the associated knowledge point to form a complete learning suggestion.

[0072] Subsequently, a structured integration and encapsulation of the mathematical modeling knowledge development report is performed: the complete multi-scale extended learning path, the key steps guiding the integrated mathematical model (including objective function, decision variables, constraints, solution algorithm and verification index), and the learning suggestions generated for all related knowledge points are arranged in the following order: first, presenting the modeling guidance for the current problem; second, showing the systematic extended learning path; and finally, listing the learning suggestions for each knowledge point in the path in detail. The final output is a structured mathematical modeling knowledge development report.

[0073] This application provides intelligent support throughout the entire process, from error analysis to weak point identification, and then to personalized guidance and path planning, which helps to improve the systematicness and pertinence of mathematical modeling learning. This application constructs an intelligent teaching framework integrating personalized diagnosis, dynamic guidance, and systematic expansion; by accurately analyzing students' bottlenecks and specific knowledge gaps in each stage of mathematical modeling, it achieves precise identification and in-depth analysis of learning weaknesses; by dynamically generating mathematical models with targeted step-by-step guidance, it effectively improves students' ability to understand and construct mathematical models; through intelligently planned personalized learning paths from remediation to expansion, it systematically consolidates and extends students' knowledge structure, and finally outputs a mathematical modeling knowledge development report integrating diagnosis, guidance, and planning. This forms a closed-loop teaching support system from accurate problem identification and real-time guidance intervention to long-term ability development, significantly enhancing the pertinence and systematicness of mathematical modeling learning.

[0074] Based on the above embodiments, referring to Figure 6 The diagram shown is a structural schematic of a multi-scale mathematical modeling system for artificial intelligence teaching. A specific system may include: The preprocessing module is used to preprocess the mathematical description text input by the user and obtain the standard mathematical problem text; The dataset construction module is used to convert historical math error records into structured data with a preset structure, and obtain the error step sequence number, error description text, deduction value, total score of the question, and knowledge point identifier to form an error sample and build an error dataset. The bottleneck distribution matrix acquisition module is used to obtain the modeling stage identifier corresponding to each wrong question sample based on the error identifier mapping rule; to count the error frequency of each knowledge point identifier in each modeling stage; to select the key bottleneck stage of each knowledge point identifier; and to form a bottleneck distribution matrix. The weakness analysis module is used to construct a knowledge point association graph based on all knowledge point identifiers in the wrong question dataset and the standard knowledge structure; obtain the error severity of each knowledge point identifier; combine the knowledge point association graph to obtain the target weakness score of each knowledge point identifier; identify and obtain the core weaknesses; and construct a knowledge point weakness topology map. The semantic element list acquisition module is used to convert standard mathematical problem text into a sequence of lexical units, input it into the mathematical semantic recognition model, extract mathematical entities and the relationships between entities, and map them to the corresponding semantic role categories to construct a semantic element list of standard mathematical problem text. The model guidance module is used to obtain the core knowledge point code based on the list of semantic elements of standard mathematical problem text and its associated knowledge point identifiers; select the key bottleneck links corresponding to the knowledge point identifiers that match the core knowledge point codes in the bottleneck distribution matrix, form a key bottleneck link identifier set, guide the basic mathematical model framework, and generate a guided integrated mathematical model. The report generation module is used to correlate and analyze the core knowledge point encoding and weak knowledge point topology map of standard mathematical problem texts, generate multi-scale extended learning paths, and combine them with guided integrated mathematical models to obtain a report on the user's mathematical modeling knowledge development.

[0075] The multi-scale mathematical modeling system for AI teaching in this embodiment is used to implement the aforementioned multi-scale mathematical modeling method for AI teaching. Therefore, the specific implementation of the multi-scale mathematical modeling system for AI teaching can be found in the embodiment section of the multi-scale mathematical modeling method for AI teaching described above. For example, the preprocessing module and the dataset construction module are used to implement steps S101 and S102 of the multi-scale mathematical modeling method for AI teaching, respectively; the bottleneck distribution matrix acquisition module is used to implement steps S103 and S104 of the multi-scale mathematical modeling method for AI teaching, respectively; the weakness analysis module and the semantic element list acquisition module are used to implement steps S105 and S106 of the multi-scale mathematical modeling method for AI teaching, respectively; the model guidance module is used to implement steps S107 and S108 of the multi-scale mathematical modeling method for AI teaching, respectively; and the report generation module is used to implement steps S109 and S110 of the multi-scale mathematical modeling method for AI teaching, respectively. Therefore, its specific implementation can be referred to the description of the corresponding embodiments, and will not be repeated here.

[0076] The multi-scale mathematical modeling method for AI teaching described in this invention, based on historical error data, breaks down the process into three main stages: model conception and definition, model construction and implementation, and model solving and verification. It generates a bottleneck distribution matrix using error frequency and adaptive threshold algorithms to accurately pinpoint weaknesses in specific modeling stages. Simultaneously, by integrating error frequency, error severity, and knowledge point correlations to calculate a weakness score, it constructs a topological map of knowledge point weaknesses, achieving in-depth analysis from single-point weaknesses to structural knowledge gaps, thus addressing the fragmented and unsystematic diagnostic problems of existing technologies. Based on semantic parsing to extract core problem elements, and combined with bottleneck diagnosis results, this invention dynamically embeds adaptive guidance content into the basic mathematical model framework. It provides targeted guidance for different bottleneck stages, including objective function analysis, constraint derivation, and algorithm step decomposition. This strongly binds the guidance content to students' weaknesses, avoiding generic assistance and achieving real-time responsiveness between modeling steps and individual weaknesses, thus overcoming the shortcomings of existing technologies that disconnect modeling support from specific knowledge gaps. This invention starts with the encoding of core knowledge points and divides the learning process into three levels—remediation, consolidation, and expansion—based on weakness scores and topological chain types. This forms a step-by-step path from supplementing prior knowledge and strengthening current core knowledge to extending downstream knowledge. The learning path is deeply integrated with the guidance model and diagnostic results to generate a structured knowledge development report. This enables full-process support for problem discovery, immediate guidance, and long-term improvement, allowing mathematical modeling learning to move from fragmented to systematic. It also provides reliable technical support for personalized support, significantly improving the efficiency and quality of teaching support.

[0077] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.

[0078] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A system that specifies functions in one or more boxes.

[0079] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including an instruction set implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0080] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0081] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A multi-scale mathematical modeling method for artificial intelligence teaching, characterized in that, include: Preprocess the mathematical description text input by the user to obtain the standard mathematical problem text; Historical math mistakes are converted into structured data with a pre-defined structure, and the sequence number of the wrong steps, the text of the error description, the deduction value, the total score of the question, and the knowledge point identifier are obtained to form a sample of wrong questions and construct a dataset of wrong questions. Based on the error identification mapping rules, obtain the modeling stage identifier corresponding to each incorrect question sample; Statistical analysis of the error frequency of each knowledge point identifier in each modeling stage; selection of the key bottleneck stages of each knowledge point identifier; formation of a bottleneck distribution matrix. Based on all the knowledge point identifiers in the incorrect question dataset and the standard knowledge structure, a knowledge point association graph is constructed; the error severity of each knowledge point identifier is obtained, and combined with the knowledge point association graph, the target weakness score of each knowledge point identifier is obtained, the core weaknesses are identified, and a knowledge point weakness topology map is constructed. Standard mathematical problem texts are converted into sequences of lexical units, input into a mathematical semantic recognition model, mathematical entities and relationships between entities are extracted, and mapped to corresponding semantic role categories to construct a list of semantic elements of standard mathematical problem texts. Based on the list of semantic elements of standard mathematical problem texts and their associated knowledge point identifiers, the core knowledge point codes are obtained; In the bottleneck distribution matrix, select the key bottleneck links corresponding to the knowledge point identifiers that match the core knowledge point codes, form a key bottleneck link identifier set, guide the basic mathematical model framework, and generate a guided integrated mathematical model. The core knowledge points encoding and weak knowledge point topology map of standard mathematical problem texts are correlated and analyzed to generate multi-scale extended learning paths. Combined with guided integrated mathematical models, a report on the user's mathematical modeling knowledge development is obtained.

2. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, Preprocess the user-input mathematical description text to obtain the standard mathematical problem text, including: Perform character-level cleaning on the mathematical description text input by the user, identify and remove irrelevant symbols and tags, and obtain the cleaned text; Based on the general standards of mathematical language, the mathematical terms, symbols and expressions in the cleaned text are converted into standard symbols and terms to obtain the converted text; Based on standard mathematical grammar rules, the operation order, function representation, bracket hierarchy, and formula layout of the converted text are restructured and formatted to obtain standard mathematical problem text.

3. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, Based on the error identification mapping rules, the modeling stage identifier corresponding to each incorrect question sample is obtained, including: Determine whether the semantics of the error description text in the sample of incorrect questions are clear: If clearly defined, then the mapping is performed based on the semantics of the incorrect description text of the incorrect question samples; If not clearly defined, mapping is performed based on the relative position of the sequence number of the incorrect steps in the incorrect question sample; The semantic mapping based on the error description text of the wrong question samples includes: if the semantics contain mathematical abstraction of the problem, definition of key variables or target assumptions, it is mapped to the model conception and definition stage; if the semantics contain the establishment of equations, inequalities or functional relationships, it is mapped to the model construction and implementation stage; if the semantics contain numerical calculation, algorithm execution, result verification or error analysis, it is mapped to the model solution and verification stage. Mapping is performed based on the relative position of the error step sequence number of the incorrect question sample, including: if the relative position is in the first 1 / 3 interval, it is mapped to the model conception and definition stage; if the relative position is in the middle 1 / 3 interval, it is mapped to the model construction and implementation stage; if the relative position is in the last 1 / 3 interval, it is mapped to the model solution and verification stage.

4. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, The error frequency of each knowledge point identifier in each modeling stage was statistically analyzed, and the key bottleneck stages of each knowledge point identifier were selected to form a bottleneck distribution matrix, including: For each knowledge point identifier, obtain the modeling steps that contain that knowledge point identifier, and count the number of times each knowledge point identifier appears in each modeling step; The ratio of the number of times each knowledge point identifier appears in any modeling stage to the total number of times it appears in all modeling stages is used as the error frequency of each knowledge point identifier in any modeling stage. Based on the error frequency of each knowledge point identifier in each modeling stage, a distribution vector is formed, and a stage threshold is constructed. For each knowledge point, identify the modeling steps whose error frequency exceeds the threshold and use them as the key bottleneck steps for each knowledge point. Identify the key bottlenecks identified in all knowledge points and construct a bottleneck distribution matrix.

5. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, The error severity of each knowledge point is obtained, and combined with the knowledge point association graph, the target weakness score of each knowledge point is obtained. Core weaknesses are identified, and a knowledge point weakness topology map is constructed, including: Using all the knowledge point identifiers after deduplication from the incorrect question dataset as nodes; using the standard knowledge structure, obtain the relationships between the knowledge point identifiers and construct connecting edges; based on all the nodes and connecting edges, form a knowledge point association graph; Calculate the ratio of the deduction value of each incorrect question sample to the total score of the question, and use it as the error score of each incorrect question sample; calculate the arithmetic mean of the error scores of each incorrect question sample belonging to the same knowledge point to obtain the error severity of each knowledge point. Based on the knowledge point association graph, an iterative update algorithm is used to calculate the weakness score of each node after a preset number of iterations, which is used as the target weakness score of the knowledge point represented by each node. Calculate the sum of the average and standard deviation of the target weakness scores for all nodes, and use it as the weakness threshold; identify the nodes whose target weakness scores are greater than the weakness threshold as core weaknesses. For each core weakness, the preceding knowledge chain, the set of knowledge points at the same level, and the downstream influence chain of each core weakness are obtained from the knowledge point association graph to form a knowledge point weakness topology graph. Specifically, the process involves recursively traversing along the in-degree direction of the core weak point to obtain the preceding nodes that are directly or indirectly connected to the core weak point, forming a preceding knowledge chain; obtaining nodes that are connected to the core weak point through undirected edges to form a flat layer knowledge point set; and recursively traversing along the out-degree direction of the core weak point to obtain the successor nodes that are directly or indirectly connected to the core weak point, forming a downstream influence chain.

6. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, Standard mathematical problem text is converted into a sequence of lexical units, input into a mathematical semantic recognition model, and mathematical entities and relationships between entities are extracted and mapped to corresponding semantic role categories. This constructs a list of semantic elements for the standard mathematical problem text, including: Using a bidirectional scanning matching word segmentation algorithm, the standard mathematical problem text is scanned in both forward and reverse directions. It is then matched with a pre-defined mathematical domain word segmentation dictionary based on the maximum length matching principle to obtain forward and reverse candidate sequences. The sequence with fewer words is selected as the word unit sequence. Based on mathematical grammar and semantic norms, structured annotation is performed on mathematical elements in mathematics textbooks, academic literature and error sample sets to obtain entity category labels and relation category labels corresponding to each mathematical element and construct training sets; Based on the training set, a mathematical semantic recognition model containing a Transformer encoder, an entity classifier, and a relation classifier is trained to obtain a trained mathematical semantic recognition model. Input the sequence of lexical units corresponding to the standard mathematical problem text into the trained mathematical semantic recognition model to obtain the entity category of each word and the relationship category between any two words, forming a set of mathematical entities and relationships. Based on the mathematical meaning they represent, each element in the set of mathematical entities and relations is mapped to a target role, variable role, constraint role, or relation role to obtain the semantic role category of each element. Normalize each element in the set of mathematical entities and relations to obtain standardized symbols; use the semantic role category, standardized symbol, and mathematical elements contained in an element as a semantic element to form a list of semantic elements.

7. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 6, characterized in that, Based on the list of semantic elements of standard mathematical problem text and their associated knowledge point identifiers, the corresponding core knowledge point codes are obtained, including: Based on a pre-defined symbol knowledge point hierarchical mapping table, standardized symbols in semantic elements are mapped to knowledge point codes, and hierarchical annotations are performed on the knowledge point codes; the hierarchical annotations include a basic operation layer, a core concept layer, and a comprehensive application layer. The comprehensive weight of each knowledge point code is calculated based on the weight of the hierarchical annotation corresponding to each knowledge point code and the semantic role weight of the semantic element. Obtain the code of the knowledge point with the highest overall weight and use it as the core knowledge point code.

8. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 6, characterized in that, Guided by the basic mathematical model framework, a guided integrated mathematical model is generated, including: In the model design and definition phase, target roles are extracted from the list of semantic elements in standard mathematical problem texts and converted into standard objective functions, and variable roles are extracted and converted into a set of decision variables. In the model building and implementation phase, constraint roles are extracted from the list of semantic elements of standard mathematical problem texts and converted into a set of constraint conditions, and relation roles are extracted and converted into a set of mathematical relations between variables. In the model solving and verification stage, based on the standard objective function and constraint set, a mathematical optimization algorithm is selected as the model solver to generate a basic mathematical model framework; The key bottleneck links are identified in the set, and the links are guided and enhanced to obtain a guided integrated mathematical model.

9. The multi-scale mathematical modeling method for artificial intelligence teaching according to claim 1, characterized in that, Association analysis of core knowledge point encoding and weak knowledge point topology maps in standard mathematical problem texts generates multi-scale extended learning paths, including: Extract all knowledge points that have a direct topological relationship with the core knowledge point encoding from the knowledge point weakness topology graph, and use them as related knowledge points; The weakness score of the related knowledge point is taken as the weakness score of the related knowledge point, based on the weakness score of the node corresponding to the related knowledge point. Based on the location of the node corresponding to the related knowledge point in the preceding knowledge chain, the same-level knowledge point set, or the downstream influence chain, obtain the topology chain type to which the related knowledge point belongs. Starting with the encoding of core knowledge points, and based on the weakness scores of each related knowledge point and the type of its topology chain, the related knowledge points are divided into remedial, consolidation, or expansion learning levels to obtain the learning order of related knowledge points and generate a multi-scale expansion learning path.

10. A system based on the multi-scale mathematical modeling method for artificial intelligence teaching as described in any one of claims 1 to 9, characterized in that, include: The preprocessing module is used to preprocess the mathematical description text input by the user and obtain the standard mathematical problem text; The dataset construction module is used to convert historical math error records into structured data with a preset structure, and obtain the error step sequence number, error description text, deduction value, total score of the question, and knowledge point identifier to form an error sample and build an error dataset. The bottleneck distribution matrix acquisition module is used to obtain the modeling stage identifier corresponding to each wrong question sample based on the error identifier mapping rule; Statistical analysis of the error frequency of each knowledge point identifier in each modeling stage; selection of the key bottleneck stages of each knowledge point identifier; formation of a bottleneck distribution matrix. The weakness analysis module is used to construct a knowledge point association graph based on all knowledge point identifiers in the wrong question dataset and the standard knowledge structure; obtain the error severity of each knowledge point identifier; combine the knowledge point association graph to obtain the target weakness score of each knowledge point identifier; identify and obtain the core weaknesses; and construct a knowledge point weakness topology map. The semantic element list acquisition module is used to convert standard mathematical problem text into a sequence of lexical units, input it into the mathematical semantic recognition model, extract mathematical entities and the relationships between entities, and map them to the corresponding semantic role categories to construct a semantic element list of standard mathematical problem text. The model guidance module is used to obtain the core knowledge point codes based on the list of semantic elements of standard mathematical problem text and its associated knowledge point identifiers; In the bottleneck distribution matrix, select the key bottleneck links corresponding to the knowledge point identifiers that match the core knowledge point codes, form a key bottleneck link identifier set, guide the basic mathematical model framework, and generate a guided integrated mathematical model. The report generation module is used to correlate and analyze the core knowledge point encoding and weak knowledge point topology map of standard mathematical problem texts, generate multi-scale extended learning paths, and combine them with guided integrated mathematical models to obtain a report on the user's mathematical modeling knowledge development.

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