A modeling case automatic generation system and method for secondary vocational mathematics teaching

Abstract

This invention belongs to the field of intelligent education technology, specifically referring to an automatic modeling case generation system and method for vocational school mathematics teaching. It includes a professional scene semantic parsing module that configures a vocational school professional word segmentation dictionary and a fuzzy semantic normalization submodule to transform non-standard colloquial expressions into standardized semantic vectors; a knowledge graph module that stores multiple professional scenes and modeling templates based on a graph database, and completes scene location and completion through a subgraph matching algorithm; a case generation engine with built-in problem context generation, mathematical model construction, and dynamic noise injection submodules that generate modeling cases with simulation data based on difficulty levels; and a learning adaptation module that uses a dual-dimensional quantitative formula to calculate five levels of difficulty and drives a dual mechanism of three-level database retrieval and real-time generation. This invention achieves deep alignment between modeling cases and professional scenarios, supports personalized difficulty adaptation, and effectively improves case generation efficiency and teaching practicality.

Description

Technical Field

[0001] This invention belongs to the field of intelligent education technology, specifically referring to an automatic modeling case generation system and method for vocational school mathematics teaching. Background Technology

[0002] Vocational education has a distinct vocational attribute, and different majors (such as cooking, mechanics, electronics, and auto repair) have significantly different requirements for mathematical knowledge. Currently, vocational mathematical modeling teaching faces the following technical challenges:

[0003] First, the modeling cases are out of touch with the profession. Existing systems generally use a general case library, which cannot generate modeling cases that are deeply integrated with specific professional scenarios.

[0004] Secondly, case generation relies on manual labor, which is inefficient and difficult to scale. Teachers need to spend a lot of time finding or compiling cases that fit the actual professional practice.

[0005] Third, existing automatic math problem generation systems mostly use template filling, lacking semantic understanding and mathematical modeling capabilities for real-world professional scenarios, resulting in generated problems that are often detached from actual production situations.

[0006] Fourth, the difficulty of the cases is fixed, and there is a lack of a dynamic perception mechanism for students' cognitive levels, making it difficult to achieve personalized tiered adaptation. This results in a common phenomenon where students with weak foundations cannot keep up, while students with outstanding abilities are not challenged enough. Summary of the Invention

[0007] To address the aforementioned challenges, this invention provides an automatic modeling case generation system and method for vocational school mathematics teaching.

[0008] To achieve the above functions, the technical solution adopted by the present invention is as follows: an automatic modeling case generation system for secondary vocational school mathematics teaching, including a professional scenario semantic parsing module, a professional knowledge graph module, a modeling case generation engine, a learning situation adaptation module, a modeling case database, and a visualization output module;

[0009] The professional scenario semantic parsing module is configured with a vocational school industry quantifier mapping table and a fuzzy semantic normalization submodule. It is used to receive professional teaching scenario description text containing non-standard colloquial numerical expressions and unit alternatives, map the non-standard expressions into standard numerical expressions with unified dimensions, and generate standardized semantic vectors after eliminating ambiguity. It extracts mathematical elements such as variables, quantitative relationships, constraints, and objective functions through natural language processing and outputs them to the knowledge graph module and case generation engine.

[0010] The occupational knowledge graph module has built-in occupational knowledge graphs for various professions, receives the mathematical elements for matching and scene completion, and outputs scene modeling information to the case generation engine.

[0011] The modeling case generation engine has an embedded dynamic noise injector. It receives difficulty parameters from the semantic parsing module, knowledge graph module, and learning adaptation module, and automatically generates modeling cases.

[0012] The learning adaptation module interacts bidirectionally with the modeling case generation engine, external user terminal, and modeling case database, respectively, and is used to dynamically adjust the difficulty based on learning data, search the database, and trigger the generation of new cases when the existing cases are insufficient.

[0013] The modeling case database is connected to the modeling case generation engine and the learning situation adaptation module. It is used to store the generated modeling cases, receive case data written by the modeling case generation engine, and provide an interface for the learning situation adaptation module to retrieve cases by difficulty tags.

[0014] The visualization output module is connected to the modeling case generation engine and the external user terminal. It is used to receive case data output by the modeling case generation engine and output the modeling cases to the user terminal in multiple formats.

[0015] Preferably, the occupational knowledge graph is stored in the form of a graph database, including professional nodes, course nodes, knowledge point nodes, occupational scenario nodes, modeling template nodes, and edges connecting the nodes. Each occupational scenario node is associated with at least one mathematical modeling task template and its corresponding difficulty coefficient.

[0016] Preferably, the occupational knowledge graph module uses a subgraph matching algorithm, which uses the mathematical elements output by semantic parsing as search conditions, and performs multi-hop relation constraint search along the associated edges to complete knowledge matching.

[0017] Preferably, the professional scenario semantic parsing module is configured with a vocational school-specific word segmentation dictionary and dependency parsing rules to extract structured mathematical elements from the descriptive text.

[0018] Preferably, the modeling case generation engine includes a problem scenario generation submodule, a mathematical model construction submodule, a data generation submodule, and a case encapsulation submodule. The problem scenario generation submodule has a built-in scenario-based question template library for generating natural language question stems. The mathematical model construction submodule has a built-in mathematical model template library for generating mathematical model expressions. The data generation submodule is used to superimpose noise linked to the difficulty level onto the theoretical values ​​of the model to generate simulation data. The case encapsulation submodule is used to integrate the generated case content into a structured data package.

[0019] Preferably, the learning adaptation module calculates the target difficulty level based on two dimensions: the average mastery level and the modeling ability level in the students' historical learning data, and prioritizes using this difficulty level as the search condition to retrieve existing cases from the modeling case database.

[0020] Preferably, the modeling case database stores structured case data packages with professional tags, difficulty tags, and knowledge point tags; after the learning adaptation module calculates the target difficulty level, it prioritizes searching for cases at that difficulty level. If the search results are insufficient, it triggers the modeling case generation engine to generate cases dynamically in real time.

[0021] Preferably, the visualization output module supports multiple output formats, including text, function graphs, and data charts.

[0022] This invention also discloses a method for automatically generating modeling cases for vocational school mathematics teaching, comprising the following steps:

[0023] S1: In response to an HTTP request sent by an external user terminal, parse the text fields in the request body payload to obtain the professional teaching scenario description text, and extract a set of mathematical elements containing variable parameters, quantitative relationships, constraints, and objective function types through semantic parsing;

[0024] S2: Input the mathematical elements into the professional knowledge graph module, and use the standardized semantic vector as the anchor point. Use the Cypher query statement to perform multi-hop association edge traversal and matching of professional nodes and scene nodes in the graph database to determine the corresponding professional fields, prerequisite knowledge points and modeling templates.

[0025] S3: Read the historical learning data of the target students, and calculate the case target difficulty level D according to the following modified formula based on the average mastery level M and the modeling ability level A.

[0026] ;

[0027] Where M is a real number from 0 to 1, A is an integer from 1 to 5, the max and min functions lock the final difficulty in the range of 1 to 5, and round is the rounding operation.

[0028] S4: Generate a case by combining the mathematical elements, the graph matching results, and the target difficulty level;

[0029] S5: Encapsulate the generated cases into a structured data package in JSON format, store it in the modeling case database, and write a record containing a difficulty index field to the database;

[0030] S6: Visualize and output the modeling case to the user terminal.

[0031] Compared with the prior art, the present invention achieves the following beneficial effects by adopting the above structure:

[0032] (1) It is equipped with a professional word segmentation dictionary and syntactic analysis rules for vocational secondary schools to accurately analyze professional terms and make up for the shortcomings of general NLP tools in adapting to vocational secondary school scenarios;

[0033] (2) Relying on multi-professional occupational knowledge graphs and subgraph matching algorithms, the fit between cases and professional scenarios is significantly improved, effectively solving the problem of cases being disconnected from professions;

[0034] (3) The two-dimensional learning quantification formula is used to realize the five-level difficulty adaptation, and the gradient Gaussian noise simulation data is used to meet the needs of tiered practical training.

[0035] (4) The dual mechanism of multi-level database retrieval and real-time generation ensures continuous output of adapted cases and guarantees uninterrupted teaching. Attached Figure Description

[0036] Figure 1 This is a flowchart of the present invention;

[0037] Figure 2 The flowchart of the professional scenario semantic parsing module and the professional knowledge graph module proposed in this invention;

[0038] Figure 3 The flowchart of the learning adaptation module and modeling case generation engine proposed in this invention;

[0039] Figure 4 The flowchart for storage retrieval and visualization output provided by this invention is shown. Detailed Implementation

[0040] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] according to Figure 1 As shown, the system of this invention adopts a B / S architecture. The server-side uses the Neo4j graph database to store the professional knowledge graph and the MySQL database to store the modeling case database. The front-end user terminals are teacher PCs and student tablets. The modules communicate and interact via HTTP and WebSocket protocols, including the following modules:

[0042] Professional Scenarios Semantic Parsing Module: This module is based on the Harbin Institute of Technology LTP Language Technology Platform and is configured with a customized word segmentation dictionary for secondary vocational schools. It is statistically verified based on the Ministry of Education's "Directory of Majors in Secondary Vocational Schools" and the teaching syllabus and industry standard terminology database of 12 major categories of mainstream majors, covering more than 8,600 professional compound terms, and is configured with dependency parsing rules.

[0043] Specifically, the professional scene semantic parsing module is also equipped with a fuzzy semantic normalization submodule, which is used to map colloquial numerical expressions (such as "a hundred or so yuan", "about 50") and unit alternatives (such as "piece", "item" and "only") to standard numerical expressions and unified dimensions, and to perform synonym replacement preprocessing before dependency parsing to reduce the failure rate of element extraction caused by non-standard expressions.

[0044] As an alternative implementation, when the third-party language platform (such as LTP) interface is unavailable, the fuzzy semantic normalization submodule automatically downgrades to a preset regular expression matching strategy. This strategy pre-compiles a regular expression library of trigger words for 12 major professional scenarios (e.g., "processing? parts" matches quantity, "cost? yuan" matches unit price), and extracts core variables based on the longest string matching algorithm. The semantic parsing module has a built-in confidence scoring submodule. When the completeness score of the elements obtained from dependency parsing is lower than a preset threshold (e.g., key variables or constraints are missing), the system automatically generates a semi-structured element set and triggers a human-machine collaborative correction interface, prompting external user terminals to select and complete unrecognized fields to eliminate the ambiguity risk caused by non-standardized spoken language. Through this dual-mode redundant architecture, the system can still complete the extraction of basic mathematical elements and case generation in an offline environment, ensuring the robustness of industrial deployment.

[0045] In the word segmentation stage: the reverse maximum matching algorithm is used to prioritize matching the longest professional terms to ensure that compound words such as "numerical control lathe" are not incorrectly segmented.

[0046] Dependency parsing rules:

[0047] ① Independent variable identification rules: If a node is a noun and forms a subject-predicate relationship with the core verb, then the node is determined to be a candidate independent variable; if there are multiple subject-predicate nouns in the sentence, then the first one is marked as the main independent variable, and the rest are marked as auxiliary variables (such as time, ordinal number, etc.).

[0048] ② Dependent variable identification rule: If the part of speech of a node is a noun and it forms a verb-object relationship with the core verb, and the noun is a measurable entity such as quantity, cost, profit, temperature, length, etc. (determined by matching the entity dictionary), then it is determined to be a dependent variable.

[0049] ③ Operational Relationship Recognition Rules: Scan core verbs and adverbs, map "each" and "unit price" to multiplication, "total" and "total" to addition, "loss" and "decline" to subtraction, and "times" and "exponent" to exponentiation, generating standardized relationship labels;

[0050] ④ Constraint identification rules: Extract the numerical boundaries in the dependency subtree containing words such as "when," "not exceeding," and "at least." For example, "maximum 100 pieces" is mapped to x≤100, and "at least 5 hours" is mapped to t≥5.

[0051] ⑤ Objective function type identification rule: Map "lowest" and "minimum" to "minimize", and "highest" and "maximum" to "maximize".

[0052] If the extracted elements are incomplete, the module will package the identified elements into a "partial element set" and mark the unidentified fields as "to be completed", and then transfer them to the knowledge graph module for completion.

[0053] The professional knowledge graph module includes 12 professional nodes, 48 ​​vocational mathematics-related course nodes, 112 mathematical knowledge point nodes, 236 professional scenario nodes, and 78 sets of modeling template nodes. The connecting edges include three types of directional relationships: professional scenario nodes connect to modeling template nodes via template edges, knowledge point nodes via prerequisite knowledge edges, and professional nodes via their respective professional edges. Each professional scenario node is associated with at least one mathematical modeling task template and its corresponding difficulty level, supporting template selection at different difficulty levels, from simple linear functions to complex piecewise functions.

[0054] The knowledge graph in this module is constructed by combining expert knowledge with textbook corpora: First, a team of vocational mathematics education experts manually annotated and structured the data based on the teaching syllabi of 12 mainstream majors, the standards of 48 vocational mathematics courses, and the description documents of 236 typical occupational scenarios, forming initial nodes and related edges; then, the weights of the related edges were statistically verified and supplemented through the co-occurrence relationships of terms in the textbook corpora; finally, all structured data was imported into the Neo4j graph database to form a searchable knowledge graph.

[0055] This module has a built-in subgraph matching and retrieval interface. In specific implementation, first, using the "objective function type label" and "number of variable parameters" as anchors, a set of candidate professional scenario nodes is located through Cypher query. Then the actual number of knowledge points contained in the input semantic parsing result is counted, and the number of overlaps between these knowledge points and the set of pre-requisite knowledge points associated with a certain professional scenario node in the knowledge graph is counted. The knowledge point coverage Cov of this scenario is obtained by dividing the number of overlaps by the total number of input knowledge points. A matching degree threshold T=70% is set, candidate nodes with Cov<T are excluded, and it is verified whether the variable dimension of the associated template is consistent with the input. If not, the priority of this candidate node is reduced. Finally, for each candidate scenario, the comprehensive matching degree is calculated by weighted summation of the knowledge point coverage (weight 0.6) and the template dimension matching flag (weight 0.4). The specific meaning of knowledge point coverage is: the proportion of overlap between the knowledge points obtained from semantic parsing and the pre-requisite knowledge points of this scenario in the knowledge graph; the template dimension matching flag is a binary variable, which is 1 when the dimensions are consistent and 0 when they are inconsistent. The one with the highest score and no less than the threshold of 70% is taken as the matching result. If the comprehensive scores of all candidate scenarios are lower than the threshold, a completion mechanism is triggered: the general default template under the major to which the scenario belongs is selected, and the knowledge graph module backfills the default knowledge points and the industry conventional constraints under this scenario.

[0056] The modeling case generation engine includes four sub-modules, and each sub-module is scheduled to run in an independent thread.

[0057] The problem scenario generation sub-module has a built-in scenario-based question stem template library in XML format. Fillable slots such as major, scenario, variable, and constraint are reserved in the template. By integrating semantic parsing and knowledge graph matching information, the extracted variable names, constraint values, and objective function descriptions are filled into the corresponding slots to form a post-specific question stem. For example, the template for the machining scenario pre-reserves slots such as "processing quantity", "fixed loss", and "raw material unit price", and a complete engineering cost accounting problem description is generated after filling.

[0058] The mathematical model construction sub-module is pre-built with (including but not limited to) five types of basic standard templates of linear function, quadratic function extremum, exponential function, piecewise function, and sequence (as a preferred embodiment), and each type of template is bound with a semantic trigger word set (for example, "cost accounting" corresponds to the structure of "total cost = fixed cost + variable cost × quantity"). During matching, templates with conflicting directions are first excluded according to the target function type direction ("minimization" or "maximization") obtained from parsing, then the target function type label and the trigger words of each remaining template are respectively subjected to TF-IDF vectorization, the cosine similarity is calculated, the template with the highest similarity is selected, and variable parameters and constraint conditions are substituted to generate a complete mathematical model expression (output in LaTeX format). The modeling case generation engine reserves a template dynamic expansion interface, which supports loading extended templates beyond the five basic templates (such as trigonometric functions and statistical regression models) on demand according to the modeling template attribute of the occupational scenario node in the professional knowledge graph, so as to adapt to the differentiated demands of different majors for mathematical branches.

[0059] Specifically, when performing template matching, the mathematical model construction sub-module first executes mandatory pre-screening of the target direction, takes "minimization" and "maximization" as hard filtering conditions, and only retains templates consistent with the direction of the target function type label to participate in the subsequent TF-IDF vectorization cosine similarity calculation, so as to eliminate directional mismatches caused by semantic synonyms (such as "cost" and "profit").

[0060] In this embodiment, the specific method for calculating the TF-IDF vectorization cosine similarity is: performing word segmentation and removing stop words (such as "de", "le", "shi", etc.) on the target function type label text and the semantic trigger word set text of the template respectively, then counting the term frequency (TF) and inverse document frequency (IDF) of each word in the corpus, representing each text as a TF-IDF weight vector with words as dimensions, and then calculating the cosine included angle value of the two vectors, which ranges from 0 to 1, and a larger value indicates closer semantics.

[0061] The data generation sub-module (dynamic noise injector) determines the noise standard deviation σ according to the target difficulty level, the mean value of Gaussian noise is 0, and the mapping relationship between the standard deviation σ and the difficulty level is: σ=0.5×D (as the system default factory mapping parameter), where D is the target difficulty level (an integer with a value from 1 to 5). On the basis of the theoretical model value, Gaussian noise obeying the N(0, σ²) distribution is superimposed to generate simulation training data. The mapping coefficient 0.5 supports dynamic reconfiguration through the system management background, allowing teachers or teaching research administrators to adjust the noise intensity according to the actual fluctuation amplitude of professional training data, so as to avoid simulation distortion caused by the mismatch between the fixed coefficient and the error distribution characteristics of specific industries (such as precision machining and extensive cooking).

[0062] Specifically, before superimposing Gaussian noise, the data generation submodule first determines the data type label (continuous or discrete integer) of each variable through semantic parsing results. If it is determined to be a discrete integer variable (such as the number of items, the number of people, or the number of vehicles), then after superimposing Gaussian noise that follows an N(0,σ²) distribution, it further performs rounding and boundary clamping operations to ensure that the generated data conforms to the actual measurement characteristics of the physical entity.

[0063] Before performing noise superposition, the data generation submodule first determines the type of independent variable based on the quantifier recognition results in semantic parsing. If the quantifier is a discrete unit of measurement such as "piece," "unit," "set," "vehicle," or "person," the variable is marked as an integer discrete type. After noise superposition, all generated values ​​of this type of variable are rounded to the nearest integer, and boundary clamping is performed using min(max(generated value, lower bound), upper bound) to ensure that discrete physical quantities (such as the number of processed pieces) do not have decimals or out-of-bounds errors. The system's preset target difficulty level and the mapping of noise standard deviation σ, and the applicable teaching scenarios are as follows: σ=0.5 is suitable for calculations in an ideal environment with almost no data fluctuations, suitable for introducing new lessons; σ=1 produces slight data jitter, cultivating preliminary data screening awareness; σ=1.5 simulates normal production errors, matching daily training data; σ=2 introduces stronger interference, containing some outlier trends, requiring modeling correction; σ=2.5 simulates a complex data environment with significant fluctuations, suitable for advanced modeling ability expansion training.

[0064] The case encapsulation submodule integrates the context text, mathematical model (LaTeX format), parameter list, constraints, simulation data array, and label information into a structured data package in JSON format for database storage and front-end output.

[0065] The learning adaptation module prioritizes reading students' historical learning data and calculates the target difficulty level D using the following correction formula:

[0066] ;

[0067] Where M is the average mastery level (the weighted average of the historical test accuracy rates of the knowledge points involved in the case, expressed as a decimal, with a value ranging from 0 to 1), A is the modeling ability level (a quantitative value of 1 to 5 based on the student's past performance in modeling problems); the max and min functions lock the final difficulty in the range of 1 to 5; round is the rounding operation.

[0068] Under this formula, D takes the exact value of 5 if and only if the student is in the extreme optimal state (M=1, A=5); and D takes the exact value of 1 if the student is in the extremely weak state (M=0, A=1), thus realizing a continuous unsaturated mapping of difficulty levels.

[0069] To prevent students with weak foundations from being overly challenged, a pre-assessment of mastery level is implemented: if M < 0.4, the effective modeling ability level is set to 40% of the original A; if 0.4 ≤ M ≤ 0.6, the effective modeling ability level = original A × (3 × M - 0.8), achieving a completely continuous transition; if M > 0.6, no suppression is implemented. Substituting the effective A into the formula D = max(1, min(5, round(M × 3.5 + effective A × 0.3))) yields the final difficulty level D. This level is also used to control the noise standard deviation and database retrieval labels. When the system is first used or the target student has no effective historical learning records (i.e., both M and A are null values), the learning adaptation module automatically initializes M and A to the preset medium level (M = 0.5, A = 3), and pushes this initialization state and the recommended difficulty level D = 3 to the external user terminal for teachers to manually overwrite and correct according to the actual learning situation.

[0070] The difficulty level D serves two purposes: as an input parameter for the noise standard deviation in σ=0.5×D; and as a search tag in the SQL WHERE clause of a database.

[0071] Database retrieval employs a three-level fault tolerance mechanism:

[0072] Level 1 search: Perform an exact search based on the target difficulty level D. If the number of hit cases is ≥3, return the results directly; if the number of hit cases is less than 3, proceed to Level 2 search.

[0073] Level 2 search: The search criteria are broadened to simultaneously search for two adjacent difficulty levels, D and D-1. If the cumulative number of hit cases is ≥3, the top 3 cases are returned after sorting by difficulty similarity; if the cumulative number of hit cases is still less than 3, the search proceeds to Level 3.

[0074] Level 3 retrieval: Skips the database and directly drives the modeling case generation engine to generate new cases in real time. During generation, a batch mode is used to generate no less than 5 variant cases with the same professional label and difficulty level but different variable parameters and constraint boundary values ​​at one time. These variant cases are written to the database in batches at the same time, which effectively fills the cache pool while ensuring the diversity of cases and avoiding repeated triggering of the computationally intensive generation process in the same teaching scenario.

[0075] The modeling case database uses a MySQL database to store structured case data packages. Each case is automatically bound to three types of tags: professional tags (such as "machining", "Chinese cuisine", "electronics and electrical engineering"), difficulty tags (levels 1 to 5), and knowledge point tags (such as "linear function" and "quadratic function maximum and minimum values"), supporting multi-condition combination retrieval.

[0076] Perform deduplication verification during warehousing: For cases under the same professional label, a joint uniqueness criterion is formed by three elements: the standardized structure of the mathematical model expression (arranging the terms in the LaTeX string in descending order of variable exponents and removing redundant spaces), the variable parameter combination (the number of variables and the sequence of names), and the constraint boundary value sequence (e.g., "0<x≤100" is extracted as a lower bound of 0 and an upper bound of 100); if all three elements are completely consistent, the new case is determined as a duplicate case and discarded; if there is any difference in any dimension of the triplet, the case is determined as a new case and stored in the database. In particular, when there is a difference in the constraint boundary value sequence and the difference amplitude exceeds a preset threshold (e.g., the relative change rate of the boundary value is greater than 10%), the case is mandatorily determined as a substantially different teaching case, so as to ensure the diversity of the case library and avoid homogenization of case resources caused by excessive duplicate checking due to slight differences in boundary values.

[0077] A visualization output module, integrated with the Matplotlib drawing engine, supports synchronous output in three forms: plain text question stem — completely presenting the case problem description in natural language; function graph — automatically drawing curve graphs, scatter graphs or bar graphs according to the mathematical model, with variable names and corresponding units marked on the coordinate axes; noise-added simulation data table — listing the independent variable values, theoretical model values, and simulation values after superimposing noise in a table form. For integer discrete variables, the values displayed in the table are all legal integer values after rounding and clamping. The combination of the above three output forms is pushed to the teacher terminal or student tablet to meet the diverse display requirements of classroom teaching and after-school practice.

[0078] Example 1: (Machining major, difficulty level D=3)

[0079] S1 Semantic parsing: The teacher inputs "A numerically controlled lathe processes shaft parts, the raw material cost of each blank is 20 yuan, the fixed loss for starting the machine tool is 120 yuan, the maximum daily processing capacity is 100 pieces, find the processing quantity when the average production cost is the lowest"; parsing and extracting the independent variable x as the processing quantity (integer discrete), the dependent variable as the average cost, the constraint 0<x≤100, and the objective function type as nonlinear cost minimization;

[0080] S2 Graph matching: Subgraph matching locates the scenario of "NC lathe machining cost accounting", associates the major "Machining", the pre-knowledge points "linear function, univariate linear maximum and minimum value", the template "linear cost modeling", and the graph module supplements the industry default loss fluctuation interval under this scenario;

[0081] S3: Learning situation calculation: Set M=0.7, A=1, since M≥0.6 no suppression is performed, D=round(0.7×3.5+1×0.3)=3, σ=1.5:

[0082] S4 Case generation: The scenario sub-module fills in the slots to generate the question stem "A CNC lathe processes shaft parts, the raw material cost is 20 yuan per piece, the fixed equipment start-up loss is 120 yuan, and the daily processing quantity does not exceed 100 pieces. Find the optimal processing quantity when the total production cost is the lowest", the mathematical model matches the linear cost template (direction pre-screening passed, cosine similarity 0.94), yielding y=120+20x (0<x≤100); the data generation sub-module superimposes N (0,1.5²) noise to generate 10 sets of simulation data, performs rounding to integer and [1,100] boundary clamping for the integer discrete variable x, and encapsulates it as a JSON data packet;

[0083] S5 Storage: Encapsulated as JSON and stored in the database, with tags of "machining", "difficulty level 3", "maximum and minimum value of fractional function";

[0084] S6 Visual output: The visualization module outputs the question stem text, a straight line graph (marking the minimum cost point at the optimal solution x=100) and a simulation data table containing only integer piece counts, and pushes them to the teacher terminal.

[0085] Embodiment 2 (Chinese food cooking scenario, difficulty level 2)

[0086] Input "Each portion of ingredients costs 8 yuan, the fixed utility cost is 50 yuan, the daily sales do not exceed 40 portions, find the meal preparation quantity when the total cost is the lowest", learning situation parameters M=0.4, A=5; M=0.4 triggers transition, effective A=5×(3×0.4-0.8)=5×0.4=2, D=round(0.4×3.5+2×0.3)=round(1.4+0.6)=2, σ=1.0, generate the linear function cost model y=50+8x, with constraint 0<x≤40, and output simulation charts and graphs containing conventional errors.

[0087] Embodiment 3 (electronics and electrical engineering scenario, difficulty level 5)

[0088] Input "Profit is in the form of a quadratic function, the production capacity does not exceed 120 pieces, and the fixed loss is 800 yuan", M=0.95, A=5, no suppression, D=round(0.95×3.5+5×0.3)=5, σ=2.5, generate a quadratic extreme value model (such as y=-2x²+240x-800), with significantly fluctuating simulation data, for high-level top-tier training.

[0089] Comparative experiment: A comparative test is carried out using the system of the present invention and the existing general mathematical problem generation system (taking the general question bank system that is traditionally based on keyword matching, not supported by a professional knowledge graph, has no learning situation adaptive mechanism and only supports plain text output as the comparison object), taking the "machining cost accounting" scenario as an example, 10 case samples are generated respectively, and a double-blind scoring method is adopted (5 secondary vocational mathematics teachers score independently according to the unified scoring rubric, then take the mean value ± standard deviation):

[0090] Technical indicators Existing comparison system This invention system Comparison results Customized professional scene recognition capabilities Not supported Supports text parsing for vocational school majors This function is available Case study relevance to vocational school majors (mean ± standard deviation) 28.0% ± 4.5% (General Question Type) 94.0% ± 2.3% (Real job scenario) An increase of 66 percentage points (t-test, p<0.01) Personalized difficulty dynamic adaptation Fixed difficulty manually, without adaptive algorithm The two-dimensional formula automatically calculates difficulty levels 1 to 5. Achieving intelligent differentiated instruction Realism of simulation training data Noise-free ideal data Simulation data for complex Gaussian noise (σ maximum 2.5) Simulated industrial, catering, and electronics production data Multi-format visualization automatic output Plain text only Integrated output of text, function graphs, and data tables Reduce teachers' workload in drawing diagrams after class Machine time for modeling case generation Each question takes approximately 15 seconds to generate (requires manual correction). Automatic generation takes no more than 3 seconds The efficiency of generating single questions is increased by 5 times, and no manual correction is required.

[0091] The above results demonstrate that the present invention significantly outperforms existing technologies in terms of professional relevance, difficulty adaptability, data simulation accuracy, output richness, and generation efficiency, thus confirming the advanced nature and practicality of the present invention.

[0092] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. An automatic modeling case generation system for vocational school mathematics teaching, characterized in that: It includes a professional scenario semantic parsing module, a professional knowledge graph module, a modeling case generation engine, a learning situation adaptation module, a modeling case database, and a visualization output module; The professional scenario semantic parsing module is configured with a vocational school industry quantifier mapping table and a fuzzy semantic normalization submodule. It is used to receive professional teaching scenario description text containing non-standard colloquial numerical expressions and unit alternatives, map the non-standard expressions into standard numerical expressions with unified dimensions, and generate standardized semantic vectors after eliminating ambiguity. It extracts mathematical elements such as variables, quantitative relationships, constraints, and objective functions through natural language processing and outputs them to the knowledge graph module and case generation engine. The occupational knowledge graph module has built-in occupational knowledge graphs for various professions, receives the mathematical elements for matching and scene completion, and outputs scene modeling information to the case generation engine. The modeling case generation engine has an embedded dynamic noise injector. It receives difficulty parameters from the semantic parsing module, knowledge graph module, and learning adaptation module, and automatically generates modeling cases. The learning adaptation module interacts bidirectionally with the modeling case generation engine, external user terminal, and modeling case database, respectively, and is used to dynamically adjust the difficulty based on learning data, search the database, and trigger the generation of new cases when the existing cases are insufficient. The modeling case database is connected to the modeling case generation engine and the learning situation adaptation module. It is used to store the generated modeling cases, receive case data written by the modeling case generation engine, and provide an interface for the learning situation adaptation module to retrieve cases by difficulty tags. The visualization output module is connected to the modeling case generation engine and the external user terminal. It is used to receive case data output by the modeling case generation engine and output the modeling cases to the user terminal in multiple formats.

2. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The professional knowledge graph is stored in the form of a graph database, which includes professional nodes, course nodes, knowledge point nodes, professional scenario nodes, modeling template nodes, and edges connecting the nodes. Each professional scenario node is associated with at least one mathematical modeling task template and its corresponding difficulty coefficient.

3. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The occupational knowledge graph module uses a subgraph matching algorithm, which takes the mathematical elements output by semantic parsing as search conditions, and performs multi-hop relation constraint search along the associated edges to complete knowledge matching.

4. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The professional scenario semantic parsing module is configured with a vocational school-specific word segmentation dictionary and dependency parsing rules to extract structured mathematical elements from the descriptive text.

5. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The modeling case generation engine includes a problem scenario generation submodule, a mathematical model construction submodule, a data generation submodule, and a case encapsulation submodule; the problem scenario generation submodule has a built-in scenario-based question template library for generating natural language question stems; The mathematical model construction submodule has a built-in mathematical model template library for generating mathematical model expressions; the data generation submodule is used to superimpose noise linked to the difficulty level onto the theoretical values ​​of the model to generate simulation data. The case encapsulation submodule is used to integrate the generated case content into a structured data packet.

6. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The learning adaptation module calculates the target difficulty level based on two dimensions: the average mastery level and the modeling ability level in the students' historical learning data. It then prioritizes using this difficulty level as the search criterion to retrieve existing cases from the modeling case database.

7. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The modeling case database stores structured case data packages with professional tags, difficulty tags, and knowledge point tags; after the learning adaptation module calculates the target difficulty level, it prioritizes searching for cases at that difficulty level. If the search results are insufficient, it triggers the modeling case generation engine to generate cases dynamically in real time.

8. The automatic modeling case generation system for vocational school mathematics teaching according to claim 1, characterized in that: The visualization output module supports multiple output formats, including text, function graphs, and data charts.

9. A method for automatically generating modeling cases for vocational school mathematics teaching according to any one of claims 1 to 8, characterized in that: Includes the following steps: S1: In response to an HTTP request sent by an external user terminal, parse the text fields in the request body payload to obtain the professional teaching scenario description text, and extract a set of mathematical elements containing variable parameters, quantitative relationships, constraints, and objective function types through semantic parsing; S2: Input the mathematical elements into the professional knowledge graph module, and use the standardized semantic vector as the anchor point. Use the Cypher query statement to perform multi-hop association edge traversal and matching of professional nodes and scene nodes in the graph database to determine the corresponding professional fields, prerequisite knowledge points and modeling templates. S3: Read the target students' historical learning data, and calculate the case target difficulty level D based on the average mastery level M and the modeling ability level A, using the following modified formula: ； Where M is a real number from 0 to 1, A is an integer from 1 to 5, the max and min functions lock the final difficulty in the range of 1 to 5, and round is the rounding operation. S4: Generate a case by combining the mathematical elements, the graph matching results, and the target difficulty level; S5: Encapsulate the generated cases into a structured data package in JSON format, store it in the modeling case database, and write a record containing a difficulty index field to the database; S6: Visualize and output the modeling case to the user terminal.

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